A novel method for the observation of membrane transporter dynamics

Impedance analysis of ion transport through supported lipid membranes doped with ionophores: a new kinetic approach

Kinetics of facilitated ion transport through planar bilayer membranes are normally analyzed by electrical conductance methods. The additional use of electrical relaxation techniques, such as voltage jump, is necessary to evaluate individual rate constants. Although electrochemical impedance spectroscopy is recognized as the most powerful of the available electric relaxation techniques, it has rarely been used in connection with these kinetic studies. According to the new approach presented in this work, three steps were followed. First, a kinetic model was proposed that has the distinct quality of being general, i.e., it properly describes both carrier and channel mechanisms of ion transport. Second, the state equations for steady-state and for impedance experiments were derived, exhibiting the input-output representation pertaining to the model's structure. With the application of a method based on the similarity transformation approach, it was possible to check that the proposed mechanism is distinguishable, i.e., no other model with a different structure exhibits the same input-output behavior for any input as the original. Additionally, the method allowed us to check whether the proposed model is globally identifiable (i.e., whether there is a single set of fit parameters for the model) when analyzed in terms of its impedance response. Thus, our model does not represent a theoretical interpretation of the experimental impedance but rather constitutes the prerequisite to select this type of experiment in order to obtain optimal kinetic identification of the system. Finally, impedance measurements were performed and the results were fitted to the proposed theoretical model in order to obtain the kinetic parameters of the system. The successful application of this approach is exemplified with results obtained for valinomycin-K(+) in lipid bilayers supported onto gold substrates, i.e., an arrangement capable of emulating biological membranes.

The asymmetric, rectifier-like I-V curve of the Na/K pump transient currents in frog skeletal muscle fibers

The Na/K pump transient currents in skeletal muscle fiber were identified using an improved double Vaseline gap voltage clamp technique. The asymmetric characteristics of the pump current-voltage relationship were studied. The definition of the Na/K pump currents was the ouabain-sensitive currents, where ouabain is a specific Na/K ATPase inhibitor. Membrane potential was held at -90 mV, the membrane resting potential. A series of stimulation pulse-pairs symmetric to the membrane resting potential were applied to the cell membrane. The summation of the currents responding to the two pulses in each pair indicates the asymmetry of the pump currents with respect to the membrane resting potential.The voltage dependence of the Na/K pump transient currents from skeletal muscle is similar to the steady-state I-V curve from either skeletal muscle fibers or cardiac muscles. It is a sigmoidal-shaped, asymmetric curve with respect to the membrane resting potential. This asymmetric, rectifier-like voltage dependence indicates that a symmetric oscillating membrane potential may generate a net, outward pump current. In other words, the Na/K pump molecules may be activated by an oscillating membrane potential.

Low frequency alternating electric fields inhibit lactose uptake in Kluyveromyces marxianus

Frequency-dependent lactose uptake via the H+/lactose symporter in an externally applied low-intensity alternating electric field was demonstrated, using tracer flux experiments. The uptake of radiolabeled lactose was significantly inhibited with the electric field-strength of 30 V/cm and at frequencies below 10 Hz.

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.

Permeation of phloretin across bilayer lipid membranes monitored by dipole potential and microelectrode measurements

The transmembrane diffusion of phloretin across planar bilayer lipid membranes is studied under steady-state conditions. Diffusion restrictions and adsorption related effects are measured independently. The adsorption of aligned phloretin dipoles generates a change in the intrinsic dipole potential difference between the inner and outer leaflets of the lipid bilayer. It is monitored by capacitive current measurements carried out with a direct current (dc) bias. The variation of the intramembrane electric field indicates a saturation of the binding sites at the membrane interface. In contrast, pH profile measurements undertaken in the immediate membrane vicinity show a constant membrane permeability. If phloretin binding and transmembrane diffusion are treated as two competitive events rather than subsequent steps in the transport queue the contradictory results become explainable. A mathematical model is developed where it is assumed that diffusing phloretin molecules are randomly oriented, i.e., that they do not contribute to the intrinsic membrane potential. Only the dipoles adsorbing onto the membrane are oriented. Based on these theory the membrane permeability is calculated from the capacitive current data. It is found to agree very well with the permeability deduced from the microelectrode measurements.

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. These results indicate that the ECC is a plausible mechanism for the recognition and processing of electric signals by proteins of the cell membrane.

Periodic forcing of a K+ channel at various temperatures

The random sequence of openings and closings of single ion channels and the channel conductances have been the object of intense study over the past two decades with a view toward illuminating the underlying kinetics of the channel protein molecules. Channels that are sensitive to voltage, such as many K(+)-selective channels, have been particularly useful, because the kinetic rates can be manipulated by changing the membrane voltage. Most such studies have been performed under stationary conditions and usually at a single temperature. Here we report the results of experiments with sinusoidal modulation of the membrane potential performed at several temperatures. Dwell time and cycle histograms, objects not normally associated with ion channel experiments, are herein reported. From the last, the transition probability densities for channel opening and closing events are obtained. A new and unusual phase anticipation is observed in the cycle histograms, and its temperature dependence is measured.

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.