Na,K-ATPase as A Brownian Motor: Electric Field-InducedConformational Fluctuation Leads to Uphill Pumping of Cation inthe Absence of ATP

Reducing ischemic kidney injury through application of a synchronization modulation electric field to maintain Na+/K+-ATPase functions

Renal ischemia-reperfusion injury is an important contributor to the development of delayed graft function after transplantation, which is associated with higher rejection rates and poorer long-term outcomes. One of the earliest impairments during ischemia is Na⁺/K⁺-ATPase (Na/K pump) dysfunction due to insufficient ATP supply, resulting in subsequent cellular damage. Therefore, strategies that preserve ATP or maintain Na/K pump function may limit the extent of renal injury during ischemia-reperfusion. Here, we applied a synchronization modulation electric field to activate Na/K pumps, thereby maintaining cellular functions under ATP-insufficient conditions. We tested the effectiveness of this technique in two models of ischemic renal injury: an in situ renal ischemia-reperfusion injury model (predominantly warm ischemia) and a kidney transplantation model (predominantly cold ischemia). Application of the synchronization modulation electric field to a renal ischemia-reperfusion injury mouse model preserved Na/K pump activity, thereby reducing kidney injury, as reflected by 40% lower plasma creatinine (1.17 ± 0.03 mg/dl) in the electric field-treated group as compared to the untreated control group (1.89 ± 0.06 mg/dl). In a mouse kidney transplantation model, renal graft function was improved by more than 50% with the application of the synchronization modulation electric field according to glomerular filtration rate measurements (85.40 ± 12.18 μl/min in the untreated group versus 142.80 ± 11.65 μl/min in the electric field-treated group). This technique for preserving Na/K pump function may have therapeutic potential not only for ischemic kidney injury but also for other diseases associated with Na/K pump dysfunction due to inadequate ATP supply.

Forces from the Portal Govern the Late-Stage DNA Transport in a Viral DNA Packaging Nanomotor

In the Phi29 bacteriophage, the DNA packaging nanomotor packs its double-stranded DNA genome into the virus capsid. At the late stage of DNA packaging, the negatively charged genome is increasingly compacted at a higher density in the capsid with a higher internal pressure. During the process, two Donnan effects, osmotic pressure and Donnan equilibrium potentials, are significantly amplified, which, in turn, affect the channel activity of the portal protein, GP10, embedded in the semipermeable capsid shell. In the research, planar lipid bilayer experiments were used to study the channel activities of the viral protein. The Donnan effect on the conformational changes of the viral protein was discovered, indicating GP10 may not be a static channel at the late stage of DNA packaging. Due to the conformational changes, GP10 may generate electrostatic forces that govern the DNA transport. For the section of the genome DNA that remains outside of the connector channel, a strong repulsive force from the viral protein would be generated against the DNA entry; however, for the section of the genome DNA within the channel, the portal protein would become a Brownian motor, which adopts the flash Brownian ratchet mechanism to pump the DNA against the increasingly built-up internal pressure (up to 20 atm) in the capsid. Therefore, the DNA transport in the nanoscale viral channel at the late stage of DNA packaging could be a consequence of Brownian movement of the genomic DNA, which would be rectified and harnessed by the forces from the interior wall of the viral channel under the influence of the Donnan effect.

Fluctuating noise drives Brownian transport

The transport properties of Brownian ratchet were studied in the presence of stochastic intensity noise in both overdamped and underdamped regimes. In the overdamped case, an analytical solution using the matrix-continued fraction method revealed the existence of a maximum current when the noise intensity fluctuates on intermediate timescale regions. Similar effects were observed for the underdamped case by Monte Carlo simulations. The optimal time-correlation for Brownian transport coincided with the experimentally observed time-correlation of the extrinsic noise in Escherichia coli gene expression and implied the importance of environmental noise for molecular mechanisms.

Hyperpolarization of the membrane potential in cardiomyocyte tissue slices by the synchronization modulation electric field

Our previous studies have shown that a specially designed, so-called synchronization modulation electric field can entrain active transporter Na/K pumps in the cell membrane. This approach was previously developed in a study of single cells using a voltage clamp to monitor the pump currents. We are now expanding our study from isolated single cells to aggregated cells in a 3-dimensional cell matrix, through the use of a tissue slice from the rat heart. The slice is about 150 μm in thickness, meaning the slices contain many cell layers, resulting in a simplified 3-dimensional system. A fluorescent probe was used to identify the membrane potential and the ionic concentration gradients across the cell membrane. In spite of intrinsic cell-to-cell interactions and the difficulty in stimulating cell aggregation in the tissue slice, the oscillating electric field increased the intracellular fluorescent intensity, indicating elevation of the cell ionic concentration and hyperpolarization of the cell membrane. Blockage of these changes by ouabain confirmed that the results are directly related to Na/K pumps. These results along with the backward modulation indicate that the synchronization modulation electric field can influence the Na/K pumps in tissue cells of a 3-dimensional matrix and therefore hyperpolarize the cell membrane.

Molecular basis for the electric field modulation of cytochrome C structure and function

Cytochrome c (Cyt) is a small soluble heme protein with a hexacoordinated heme and functions as an electron shuttle in the mitochondria and in early events of apoptosis when released to the cytoplasm. Using molecular dynamics simulations, we show here that biologically relevant electric fields induce an increased mobility and structural distortion of key protein segments that leads to the detachment of the sixth axial ligand Met80 from the heme iron. This electric-field-induced conformational transition is energetically and entropically driven and leads to a pentacoordinated high spin heme that is characterized by a drastically lowered reduction potential as well as by an increased peroxidase activity. The simulations provide a detailed atomistic picture of the structural effects of the electric field on the structure of Cyt, which allows a sound interpretation of recent experimental results. The observed conformational change may modulate the electron transfer reactions of Cyt in the mitochondria and, furthermore, may constitute a switch from the redox function in the respiratory chain to the peroxidase function in the early events of apoptosis.

Membrane potential hyperpolarization in Mammalian cardiac cells by synchronization modulation of Na/K pumps

In previously reported work, we developed a new technique, synchronization modulation, to electrically activate Na/K pump molecules. The fundamental mechanism involved in this technique is a dynamic entrainment procedure of the pump molecules, carried out in a stepwise pattern. The entrainment procedure consists of two steps: synchronization and modulation. We theoretically predicted that the pump functions can be activated exponentially as a function of the membrane potential. We have experimentally demonstrated synchronization of the Na/K pump molecules and acceleration of their pumping rates by many fold through use of voltage-clamp techniques, directly monitoring the pump currents. We further applied this technique to intact skeletal muscle fibers from amphibians and found significant effects on the membrane resting potential. Here, we extend our study to intact mammalian cardiomyocytes. We employed a noninvasive confocal microscopic fluorescent imaging technique to monitor electric field-induced changes in ionic concentration gradient and membrane resting potential. Our results further confirm that the well-designed synchronization modulation electric field can effectively accelerate the Na/K pumping rate, increasing the ionic concentration gradient across the cell membrane and hyperpolarizing the membrane resting potential.

Low-frequency velocity correlation spectrum of fluid in a rectangular microcapillary

In addition to the fast correlation for local stochastic motion, the velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time-tail decay. At late times, the flow approaches that of an incompressible fluid. Here, we consider the motion of a viscous fluid, at constant temperature, in a rectangular semipermeable channel. The fluid is driven through the rectangular capillary by a uniform main pressure gradient. Tiny pressure gradients are allowed perpendicular to the main flux. We solve numerically the three-dimensional Navier-Stokes equations for the velocity field to obtain the steady solution. We then set and solve the Langevin equation for the fluid velocity. We report hydrodynamic fluctuations for the center-line velocity together with the corresponding relaxation times as a function of the size of the observing region and the Reynolds number. The effective diffusion coefficient for the fluid in the microchannel is also estimated (Deff = 1.43 x 10(-10) m2.s-1 for Re = 2), which is in accordance with measurements reported for a similar system (Stepisnik, J.; Callaghan, P. T. Physica B 2000, 292, 296-301; Stepisnik, J.; Callaghan, P. T. Magn. Reson. Imaging 2001, 19, 469-472).

Entrainment of Na/K pumps by a synchronization modulation electric field

We studied entrainment of the catalytic cycle of the Na/K pumps by an imposed external AC electric field. Our results show that a well designed dichotomous oscillating electric field with a frequency close to the pumps' natural turnover rate can synchronize the pump molecules. Characteristics of the synchronized pumps include: (1) outward pump currents responding to Na-extrusion and inward pump currents responding to K-pumping in are separated; (2) magnitude of the outward pump currents can be up to three times higher than that of the randomly paced pump currents; (3) magnitude ratio of the outward over inward pump currents reveals the 3:2 stoichiometry of the pumps. We, further, gradually increased the field oscillating frequency in a stepwise pattern and kept pump synchronization in each step. We found that the pumps' turnover rate could be modulated up as the field frequency increased. Consequently, the pump currents significantly increased by many fold. In summary, these results show that the catalytic cycle of Na/K pumps can be synchronized and modulated by a well designed oscillating electric field resulting in activation of the pump functions.

Numerical methods for the stochastic Landau-Lifshitz Navier-Stokes equations

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several computational fluid dynamics approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the piecewise parabolic method) and are found to give good results for the variance of momentum fluctuations. However, neither of these schemes accurately reproduces the fluctuations in energy or density. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce fluctuations in density, energy, and momentum. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS solver are compared with theory, when available, and with molecular simulations using a direct simulation Monte Carlo algorithm.

Electrical Activation of Na/K Pumps Can Increase Ionic Concentration Gradient and Membrane Resting Potential

It has been previously demonstrated by our group that our specifically designed synchronization modulation electric field can dynamically entrain the Na/K ATPase molecules, effectively accelerating the pumping action of these molecules. The ATPase molecules are first synchronized by the field, and subsequently their pumping rates are gradually modulated in a stepwise pattern to progressively higher and higher levels. Here, we present results obtained on application of the field to intact twitch skeletal muscle fibers. The ionic concentration gradient across the cell membrane was monitored, with the membrane potential extrapolated using a slow fluorescent probe with a confocal microimaging technique. The applied synchronization-modulation electric field is able to slowly but consistently increase the ionic concentration gradient across the membrane and, hence, hyperpolarize the membrane potential. All of these results were fully eliminated if ouabain was applied to the bathing solution, indicating a correlation with the action of the Na/K pump molecules. These results in combination with our previous results into the entrainment of the pump molecules show that the synchronization-modulation electric field-induced activation of the Na/K pump functions can effectively increase the ionic concentration gradient and the membrane potential.

Synchronization modulation of Na/K pump molecules can hyperpolarize the membrane resting potential in intact fibers

Previously, we have theoretically studied the possibility of electrical rhythmic entrainment of carrier-mediated ion transporters, and experimentally realized synchronization and acceleration of the Na/K pumping rate in the cell membrane of skeletal muscle fibers by a specially designed synchronization modulation electric field. In these studies we either used cut fibers under a voltage clamp or intact fibers, but in the presence of ion channels blockers. A question remained as to whether the field-induced activation observed in the pump molecules could effectively increase the intracellular ionic concentration and the membrane potential at physiological conditions. In this paper, we studied the effects of the field on intact fibers without any channel blockers. We monitored the field-induced changes in the ionic concentration gradient across the cell membrane and the membrane potential non-invasively by using a fluorescent probe and confocal microscopic imaging techniques. The results clearly show that the entrainment of the pump molecules by the synchronization modulation electric field can effectively increase the ionic concentration gradient, and hence, hyperpolarize the membrane potential.

Synchronization of Na/K pump molecules by a train of squared pulses

We experimentally studied the Na/K pump currents evoked by a train of squared pulses whose pulse-duration is about the time course of Na-extrusion at physiological conditions. The magnitude of the measured pump current can be as much as three-fold of that induced by the traditional single pulse measurement. The increase in the pump current is directly dependent on the number of pre-pulses. The larger the number of the pre-pulses is, the higher the current magnitude can be obtained. At a particular number of pre-pulses, the pump current becomes saturated. These results suggest that a large number of pre-pulses may synchronize the pump molecules to work at the same pace. As a result, the pump molecules may extrude Na ions at the same time corresponding to the stimulation pulses, and pump in K ions at the same time during the pulse intervals. Therefore, the measured pump current is three-fold of that measured by a single pulse where the outward and inward pump currents are canceled each other.

Electroendocytosis: exposure of cells to pulsed low electric fields enhances adsorption and uptake of macromolecules

This study demonstrates alteration of cell surface, leading to enhanced adsorption of macromolecules (bovine serum albumin (BSA), dextran, and DNA), after the exposure of cells to unipolar pulsed low electric fields (LEF). Modification of the adsorptive properties of the cell membrane also stems from the observation of LEF-induced cell-cell aggregation. Analysis of the adsorption isotherms of BSA-fluorescein isothiocyanate (FITC) to the surface of COS 5-7 cells reveals that the stimulated adsorption can be attributed to LEF-induced increase in the capacity of both specific and nonspecific binding. The enhanced adsorption was consequently followed by increased uptake. At 20 V/cm the maximal binding and subsequent uptake of BSA-FITC attached to specific sites are 6.5- and 7.4-fold higher than in controls, respectively. The nonspecific LEF-induced binding and uptake of BSA are 34- and 5.2-fold higher than in controls. LEF-enhanced adsorption is a temperature-independent process, whereas LEF-induced uptake is a temperature-dependent one that is abolished at 4 degrees C. The stimulation of adsorption and uptake is reversible, revealing similar decay kinetics at room temperature. It is suggested that electrophoretic segregation of charged components in the outer leaflet of the cell membrane is responsible for both enhanced adsorption and stimulated uptake via changes of the membrane elastic properties that enhance budding and fission processes.

Redox and conformational equilibria and dynamics of cytochrome c at high electric fields

Cytochrome c (Cyt-c) adsorbed in the electrical double layer of the Ag electrode/electrolyte interface has been studied by stationary and time-resolved surface-enhanced resonance Raman spectroscopy to analyse the effect of strong electric fields on structure and reaction equilibria and dynamics of the protein. In the potential range between +0.1 and -0.55 V (versus saturated calomel electrode), the adsorbed Cyt-c forms a potential-dependent reversible equilibrium between the native state B1 and a conformational state B2. The redox potentials of the bis-histidine-coordinated six-coordinated low-spin and five-coordinated high-spin substates of B2 were determined to be -0.425 and -0.385 V, respectively, whereas the additional six-coordinated aquo-histidine-coordinated high-spin substate was found to be redox-inactive. The redox potential for the conformational state B1 was found to be the same as in solution in agreement with the structural identity of the adsorbed B1 and the native Cyt-c. For all three redox-active species, the formal heterogeneous electron transfer rate constants are small and of the same order of magnitude (3-13 s-1), which implies that the rate-limiting step is largely independent of the redox-site structure. These findings, as well as the slow and potential-dependent transitions between the various conformational (sub-)states, can be rationalized in terms of an electric field-induced increase of the activation energy for proton-transfer steps linked to protein structural reorganisation. Further increasing the electric field strength by shifting the electrode potential above +0.1 V leads to irreversible structural changes that are attributed to an unfolding of the polypeptide chain.