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

Synchronization Modulation of Na/K Pumps Induced Membrane Potential Hyperpolarization in Both Physiological and Hyperkalemic Conditions

The capability of the synchronization modulation (SM) technique in enhancing the function of Na/K pumps has been demonstrated in various cells and tissues, including cardiomyocytes, a monolayer of cultured MDCK kidney cells, peripheral blood vessels, and frog skeletal muscles. This study characterized the membrane potential hyperpolarization induced by SM in both physiological and high [K⁺]_o conditions on single skeletal muscle fibers. The results showed that SM could consistently induce membrane potential hyperpolarization by a few millivolts, and this hyperpolarization was not possible in the presence of ouabain. In contrast, the same electrical pulses but with random frequencies, constant frequencies, or synchronization with backward-modulation could not hyperpolarize the membrane potential. Prolonged field application and higher field intensity enhanced the effects of SM-induced hyperpolarization. Finally, the effect of SM was tested on skeletal muscle fibers incubated in a solution with high external potassium. Results showed that the SM electric field could hyperpolarize the membrane potential even if the external K⁺ concentration was higher than the normal, which implied the therapeutic effects of the SM electric field on the hyperkalemic situation.

Stochastically pumped adaptation and directional motion of molecular machines

Recent developments in synthetic molecular motors and pumps have sprung from a remarkable confluence of experiment and theory. Synthetic accomplishments have facilitated the ability to design and create molecules, many of them featuring mechanically bonded components, to carry out specific functions in their environment-walking along a polymeric track, unidirectional circling of one ring about another, synthesizing stereoisomers according to an external protocol, or pumping rings onto a long rod-like molecule to form and maintain high-energy, complex, nonequilibrium structures from simpler antecedents. Progress in the theory of nanoscale stochastic thermodynamics, specifically the generalization and extension of the principle of microscopic reversibility to the single-molecule regime, has enhanced the understanding of the design requirements for achieving strong unidirectional motion and high efficiency of these synthetic molecular machines for harnessing energy from external fluctuations to carry out mechanical and/or chemical functions in their environment. A key insight is that the interaction between the fluctuations and the transition state energies plays a central role in determining the steady-state concentrations. Kinetic asymmetry, a requirement for stochastic adaptation, occurs when there is an imbalance in the effect of the fluctuations on the forward and reverse rate constants. Because of strong viscosity, the motions of the machine can be viewed as mechanical equilibrium processes where mechanical resonances are simply impossible but where the probability distributions for the state occupancies and trajectories are very different from those that would be expected at thermodynamic equilibrium.

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.

Stochastic pumping of ions based on colored noise in bacterial channels under acidic stress

Fluctuation-driven ion transport can be obtained in bacterial channels with the aid of different types of colored noise including the biologically relevant Lorentzian one. Using the electrochemical rectification of the channel current as a ratchet mechanism we observe transport of ions up to their concentration gradient under conditions similar to that met in vivo, namely moderate pH gradients and asymmetrically charged lipid membranes. We find that depending on the direction of the concentration gradient the channel can pump either cations or anions from the diluted side to the concentrated one. We discuss the possible relevance of this phenomenon for the pH homeostasis of bacterial cells.

The Physics and Physical Chemistry of Molecular Machines

The concept of a "power stroke"-a free-energy releasing conformational change-appears in almost every textbook that deals with the molecular details of muscle, the flagellar rotor, and many other biomolecular machines. Here, it is shown by using the constraints of microscopic reversibility that the power stroke model is incorrect as an explanation of how chemical energy is used by a molecular machine to do mechanical work. Instead, chemically driven molecular machines operating under thermodynamic constraints imposed by the reactant and product concentrations in the bulk function as information ratchets in which the directionality and stopping torque or stopping force are controlled entirely by the gating of the chemical reaction that provides the fuel for the machine. The gating of the chemical free energy occurs through chemical state dependent conformational changes of the molecular machine that, in turn, are capable of generating directional mechanical motions. In strong contrast to this general conclusion for molecular machines driven by catalysis of a chemical reaction, a power stroke may be (and often is) an essential component for a molecular machine driven by external modulation of pH or redox potential or by light. This difference between optical and chemical driving properties arises from the fundamental symmetry difference between the physics of optical processes, governed by the Bose-Einstein relations, and the constraints of microscopic reversibility for thermally activated processes.

Thermal enhancement and stochastic resonance of polaron ratchets

We study the ratchet drift of large polarons (solitons) in molecular diatomic chains induced by unbiased time periodic electric fields at nonzero temperature below its critical value. We show that, at a nonzero temperature, the critical value of the intensity of the electric field above which the ratchet phenomenon takes place is lower than at zero temperature for the same frequency of the field. We show that there is a range of temperatures for which the polaron drift is larger than that at zero temperature. We also show that temperature decreases the value of the lowest critical period of the field. And, finally, we demonstrate that there is a stochastic resonance in a polaron ratchet, namely that there is an optimal temperature at which the polaron drift is a maximum. The values of the stochastic resonance temperature, the lowest critical values of the field intensity, and its period depend on various parameters of the system and, in particular, on the anisotropy of the chain parameters. This temperature induced decrease of the critical value of the field intensity and its period, as well as the stochastic resonance itself, may be important for practical applications of the ratchet phenomenon in systems involving conducting polymers and other low-dimensional materials. They may also be important in some biological macromolecules where the ratchet phenomenon could take place in biomotors and energy and/or charge transport.

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

Na,K-ATPase uses chemical bond energy of ATP to pump K(+) into, andNa(+) out of a cell. Both are uphill transports. During the catalyticcycle the enzyme alternates between two conformational states, E(1) andE(2). This communication describes an experiment, which employs electricfield to drive oscillation or fluctuation of enzyme conformation betweenthe E(1) and the E(2) states. It is shown that the field-inducedconformational oscillation or fluctuation leads to uphill pumping of thecation by the enzyme without consumption of ATP. Biochemical specificityof the catalysis is preserved. Data indicate that Na,K-ATPase can harvestenergy from the applied electric field to perform chemical work, and aratchet mechanism is inherent in this energy transduction process. ATheory of Electroconformational Coupling (TEC) that embodies essentialfeatures of the Brownian Ratchet successfully simulates the field-frequencyand field-amplitude optima and other features of the ion pumping activity.A four-state TEC motor can achieve high efficiency of the energytransduction, asymptotically reaching 100% under the optimal condition.Pumping by ion rectification fails to reach high efficiency. The TECconcept is also mused to understand other biological motors and engines.

Effect of alternating magnetic field treatments on enzymatic parameters of cellulase

BACKGROUND

Cellulase is an enzyme of the glycosyl hydrolase family that catalyses the cleavage of β-1,4 glycosidic bonds in cellulose. In this study an alternating magnetic field was applied to evaluate cellulase activity using carboxymethyl cellulose (CMC) as substrate.

RESULTS

The maximum and minimum activities of cellulase occurred when magnetic fields of 2.2 and 4.2 mT respectively were applied for 20 min. Following these treatments, the enzymatic parameters K(m) and V(m) were determined based on fitting to the Michaelis-Menten equations. Generally, K(m) showed the opposite trend to V(m) under magnetic field treatments. Treatment of enzyme/substrate solutions at 4.2 mT inhibited enzyme activity whereas treatment at 2.2 mT promoted it.

CONCLUSION

It appears that treating enzyme/substrate solutions with different magnetic fields can inhibit or promote enzyme activity. Further research is needed to determine how the magnetic field influences the enzyme and substrate.

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.

Theoretic, experimental, clinical bases of the water oscillator hypothesis in near-infrared photobiomodulation

The objective of this review is to propose and document a role for the water oscillator in near-infrared (NIR) photobiomodulation. Greater understanding of the role of the water oscillator may add to a more-coherent description of central effects of NIR light on redox centers and key transmembrane enzymes such as cytochrome c oxidase (CcO). In addition, water provides a complementary pathway for absorption and transportation of NIR energy in photobiomodulation. Because of its unexpected potential, we propose terming it the "water oscillator paradox." Photobiologic mechanisms involved in the treatment of complex diseases are discussed in light of the present state of the art.

Allosteric model of an ion pump

We present a simple model of a free-energy transducer made of allosterically coupled two ratchet subsystems. Each of the subsystems transports particles from one particle reservoir to another. The coupling of the subsystems imposes correlated transitions of the potential profiles of the two subsystems. As a result, a downhill flux in one subsystem with higher chemical-potential difference drives an uphill flux in the other subsystem with lower chemical-potential difference. The direction of the driven flux inverts depending on the direction of the driving flux. The ratio between the fluxes conveyed by the two subsystems is variable and nonstoichiometric. By selecting appropriate parameters, the maximum ratio of the driven flux to driving flux and maximum free-energy transducing efficiency reaches some 90 and 40%, respectively. At a stalled state, the driven flux vanishes while the driving flux remains finite. The allosteric model enables explicit analysis of the timing between binding-unbinding of particles and transitions of potential profile. The behavior of the model is similar to but different from that of the alternate access model, which is a biochemical model for active transport proteins. Our model works also as a regulatory system. We suggest that the correlated transitions of the subsystems (subunits or domains) through allosteric interaction are the origin of the diverse functions of the protein machineries.

MAGNETIC STIMULATION OF THE BRAIN INCREASE Na+, K+-ATPase ACTIVITY DECREASED BY INJECTION OF AlCl3INTO NUCLEUS BASALIS MAGNOCELLULARIS OF RATS

This article reports here on the influence of the static magnetic fields (MFs), locally applied to the brain area, on Na, K-ATPase activity in the rat with lesioned nucleus basalis magnocellularis (NBM) by intracerebral injection of 5 microl, 1% AlCl3 into the nucleus. Two AKMA micromagnets (M) flux density of 60 miliTesla, 5 mm in diameter, were bilaterally implanted with "N" polarity facing down to the cranial bones in the vicinity of the pineal gland (PG), immediately after the lesioning of NBM, during the same operation procedure. Ten days after the lesions of NBM, Na, K-ATPase activity on the erythrocyte membranes in the peripheral blood, measured spectrophotometrically, was completely inhibited. Magnetic stimulation (60 mT) of the brain during the 10 days significantly increased Na, K-ATPase activity on the erythrocyte membranes of rats with lesioned NBM. This results suggests that altered by lesions Na, K-ATPase activity in an experimental model of Alzheimer's disease might be ameliorated by magnetic stimulation of the brain.

Biophysical effects of electric fields on membrane water interfaces: a mini review

Lipid-water interfaces are dielectric transition regions. Their local organizations are highly sophisticated. They are sensitive to electric field with dramatic consequences on the global membrane organization and function. The importance of using local values of parameters (e.g. dielectric constant) near water-solution interface due to hydration and different electrostatic effects is often neglected in the description of cellular functions. Structural changes in the lipid layer are induced by minute changes in the electric properties of the interface. They bring alterations in the structure and oligomerization of membrane proteins.

Hypothesis of the cause and development of neoplasms

Cancer, in general, is considered a disease of genetic mutation. Many questions are, however, unanswered. How exactly do mutations occur in the cells? How do gene mutations interface with the cell microenvironment and macroenvironment to create cancer phenotypes? Is mutation the cause of cancer or the consequence of special adaptive responses to aging; hormonal imbalance; physical, chemical and biologic stresses and damage? What makes cancer spread in the body and invade other organs causing death to the patient? In this paper, we hypothesize that the cellular hyperexcitability via stimulation of mineral channels (e.g. sodium voltage-gated channels) and ligand excitatory receptors (e.g. glutamate and other neuron and non-neuronal excitatory receptors) could be a significant causative and pathogenic factor of cancer. Managing hyperexcitatory states of the cells through lifestyle, nutritional changes, phytochemical and pharmaceutical medications theoretically could be a prospective direction in cancer prevention and therapy.

Design principles for Brownian molecular machines: how to swim in molasses and walk in a hurricane

Protein molecular motors-perfected over the course of millions of years of evolution-play an essential role in moving and assembling biological structures. Recently chemists have been able to synthesize molecules that emulate in part the remarkable capabilities of these biomolecular motors (for extensive reviews see the recent papers: E. R. Kay, D. A. Leigh and F. Zerbetto, Angew. Chem., Int. Ed., 2006, 46, 72-191; W. R. Browne and B. L. Feringa, Nat. Nanotechnol., 2006, 1, 25-35; M. N. Chatterjee, E. R. Kay and D. A. Leigh, J. Am. Chem. Soc., 2006, 128, 4058-4073; G. S. Kottas, L. I. Clarke, D. Horinek and J. Michl, Chem. Rev., 2005, 105, 1281-1376; M. A. Garcia-Garibay, Proc. Natl. Acad. Sci., U. S. A., 2005, 102, 10771-10776)). Like their biological counterparts, many of these synthetic machines function in an environment where viscous forces dominate inertia-to move they must "swim in molasses". Further, the thermal noise power exchanged reversibly between the motor and its environment is many orders of magnitude greater than the power provided by the chemical fuel to drive directed motion. One might think that moving in a specific direction would be as difficult as walking in a hurricane. Yet biomolecular motors (and increasingly, synthetic motors) move and accomplish their function with almost deterministic precision. In this Perspective we will investigate the physical principles that govern nanoscale systems at the single molecule level and how these principles can be useful in designing synthetic molecular machines.

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.

Rotary motor powered by stochastic uncorrelated dipoles

It is demonstrated that the stochastic back-and-forth vibrations of uncorrelated dipoles may lead to rotation of their ambient dipoles. This peculiar phenomenon is clarified by considering spatial and temporal symmetry breakings. The former asymmetry is the result of the multiple biased Hamiltonian vector fields, which is a ratchet effect, and the latter, of the time sequence specified by a metastable state. Since this driving mechanism is simpler than that of F0F1ATPase, it could benefit the design of nanometer scale rotary devices.

H-NMR spin-lattice and correlation times of burned soft-tissue after treatment with an infrared pulsed laser device

BACKGROUND AND OBJECTIVES

The aim of this study was to investigate the spin-lattice (T(1), 1/T(1)) and correlation times (tau(c)) of burned soft-tissue after treatment with an infrared (IR) pulsed laser device (IPLD, 904 nm pulsed at 3 MHz).

STUDY DESIGN/MATERIALS AND METHODS

Seven groups (GI-GVII), each consisting of four albino rats, were used. Groups I-VI were anesthetized and burned with a hot tip: GI, GIII, GV were not irradiated; GII, GIV, GVI were irradiated at 0; 0 and 24; and 0, 24, and 48 hours, respectively. A control group (GVII) was neither burned nor irradiated. Samples from all groups were evaluated using a 90 MHz hydrogen nuclear magnetic resonance (H-NMR) spectrometer. An unpaired Student's t-test and an ANOVA I were preformed (alpha = 0.05).

RESULTS

At 0 and 24 hours, 1/T(1) and tau(c) data revealed significant differences between GVII and both the non-irradiated (GI, GIII), and irradiated (GII, GIV) groups. At 48 hours, only the difference in tau(c) between GVII and the irradiated group (GVI) remained significant.

CONCLUSIONS

Spin-lattice data reflected significant changes in tissues induced by the burn and a tendency towards control values for all burned groups. Meanwhile, the tau(c) value of GVI suggests the possibility of enhanced reparative effects attributable to chaotic intra- and inter-molecular energy transport to biopolymers in injured soft-tissue.

Stochastic resonance in a biological motor under complex fluctuations

The dynamics division approach proposed in this work enables us to handle dynamical equations with complex fluctuations. A Brownian motor with cyclic conformational changes is analyzed to understand effects of noise on its signal transduction, and on condition in which stochastic resonance may take place. The result reproduces several features of the experimental data on the electric activation of ion pumping by Na, K-ATPase.

Adiabatic pumping mechanism for ion motive ATPases

An ion motive ATPase is a membrane protein that pumps ions across the membrane at the expense of the chemical energy of adenosine triphosphate (ATP) hydrolysis. Here we describe how an external electric field, by inducing transitions between several protein configurations, can also power this pump. The underlying mechanism may be very similar to that of a recently constructed adiabatic electron pump [Science 283, 1905 (1999)]].

Cellular target of weak magnetic fields: ionic conduction along actin filaments of microvilli

The interaction of weak electromagnetic fields (EMF) with living cells is a most important but still unresolved biophysical problem. For this interaction, thermal and other types of noise appear to cause severe restrictions in the action of weak signals on relevant components of the cell. A recently presented general concept of regulation of ion and substrate pathways through microvilli provides a possible theoretical basis for the comprehension of physiological effects of even extremely low magnetic fields. The actin-based core of microfilaments in microvilli is proposed to represent a cellular interaction site for magnetic fields. Both the central role of F-actin in Ca2+ signaling and its polyelectrolyte nature eliciting specific ion conduction properties render the microvillar actin filament bundle an ideal interaction site for magnetic and electric fields. Ion channels at the tip of microvilli are connected with the cytoplasm by a bundle of microfilaments forming a diffusion barrier system. Because of its polyelectrolyte nature, the microfilament core of microvilli allows Ca2+ entry into the cytoplasm via nonlinear cable-like cation conduction through arrays of condensed ion clouds. The interaction of ion clouds with periodically applied EMFs and field-induced cation pumping through the cascade of potential barriers on the F-actin polyelectrolyte follows well-known physical principles of ion-magnetic field (MF) interaction and signal discrimination as described by the stochastic resonance and Brownian motor hypotheses. The proposed interaction mechanism is in accord with our present knowledge about Ca2+ signaling as the biological main target of MFs and the postulated extreme sensitivity for coherent excitation by very low field energies within specific amplitude and frequency windows. Microvillar F-actin bundles shielded by a lipid membrane appear to function like electronic integration devices for signal-to-noise enhancement; the influence of coherent signals on cation transduction is amplified, whereas that of random noise is reduced.

Ratchet models using driving forces generated by deterministic chaotic maps

This study investigates how ratchets perform under driving forces generated by the circle, baker, and logistic maps with varying driving frequencies. The markedly different unidirectional net transports induced by distinct maps and frequencies are clarified by vector field analysis of the ratchet equations. Analysis results indicate that both the deterministic property of the driving forces and the asymmetric effect due to the ratchet potential impact the transport. Moreover, the driving frequency determines which factor suppresses the other one and dominates the ratchet transport.

Constructive role of noise in signal transmissions by biomembrane proteins

We discuss new examples of the constructive role of environmental fluctuations in biophysical processes, namely quantitative enhancement and qualitative sharpening of the outgoing signal in the intercellular signal transduction, e.g., in the synaptic links. An experimental check in a chemical flow reactor is suggested.

The role of thermal activation in motion and force generation by molecular motors

The currently accepted mechanism for ATP-driven motion of kinesin is called the hand-over-hand model, where some chemical transition during the ATP hydrolysis cycle stretches a spring, and motion and force production result from the subsequent relaxation. It is essential in this mechanism for the moving head of kinesin to dissociate, while the other head remains firmly attached to the microtubule. Here we propose an alternative Brownian motor model where the action of ATP modulates the interaction potential between kinesin and the microtubule rather than a spring internal to the kinesin molecule alone. In this model neither head need dissociate (which predicts that under some circumstances a single-headed kinesin can display processive motion) and the transitions by which the motor moves are best described as thermally activated steps. This model is consistent with a wide range of experimental data on the force-velocity curves, the one ATP to one-step stoichiometry observed at small load, and the stochastic properties of the stepping.

Noise-based switches and amplifiers for gene expression

The regulation of cellular function is often controlled at the level of gene transcription. Such genetic regulation usually consists of interacting networks, whereby gene products from a single network can act to control their own expression or the production of protein in another network. Engineered control of cellular function through the design and manipulation of such networks lies within the constraints of current technology. Here we develop a model describing the regulation of gene expression and elucidate the effects of noise on the formulation. We consider a single network derived from bacteriophage lambda and construct a two-parameter deterministic model describing the temporal evolution of the concentration of lambda repressor protein. Bistability in the steady-state protein concentration arises naturally, and we show how the bistable regime is enhanced with the addition of the first operator site in the promotor region. We then show how additive and multiplicative external noise can be used to regulate expression. In the additive case, we demonstrate the utility of such control through the construction of a protein switch, whereby protein production is turned "on" and "off" by using short noise pulses. In the multiplicative case, we show that small deviations in the transcription rate can lead to large fluctuations in the production of protein, and we describe how these fluctuations can be used to amplify protein production significantly. These results suggest that an external noise source could be used as a switch and/or amplifier for gene expression. Such a development could have important implications for gene therapy.

Effects of nonequilibrium fluctuations on ionic transport through biomembranes

We investigate the effects of nonequilibrium fluctuations on ionic transport through ion channels in membranes using the concept of localized ratchet. Due to the localization, the ionic population in the binding site can be enhanced or suppressed depending upon ionic potential and its fluctuations, affecting the gating kinetics of the channel. The localized dichotomic fluctuations of ionic potential are shown to give rise to a current reversal differing from the results of periodic ratchets. It is also found that strong correlations between binding energy and membrane potential fluctuations induce resonancelike behaviors in ionic current as the fluctuating rate varies.

Diffusion in discrete ratchets

The phenomenon of noise-induced transport in ratchet devices offers an explanation for directed motion on the molecular scale observed in many biological systems. Net transport through a series of discrete states, occurring in cyclic processes or reactions, can be related to widely investigated continuous ratchet models in the context of thermally activated transitions. The transport process can be described effectively in terms of two characteristic coefficients: velocity and diffusion. Their relation to model parameters and limitations for the ratchet mechanism are discussed in this paper. As an application we consider a four-state model for uphill transmembrane transport and compare theoretical results with existing data from a related experiment.

Overview: The constructive role of noise in fluctuation driven transport and stochastic resonance

Random noise is typically thought of as the enemy of order rather than as a constructive influence. Recent work has shown however that under certain circumstances, noise and Brownian motion can facilitate transmission of information via a mechanism know as stochastic resonance, and help systems use chemical energy and nonequilibrium fluctuations to drive directed motion via fluctuation driven transport. In this focus issue we have collected several articles that capture the flavor of these developing fields and point the way to new directions for research. (c) 1998 American Institute of Physics.

Barrier fluctuations and stochastic resonance in membrane transport

The role of barrier fluctuations in membrane enzymatic processes, in particular in the active transport of ions through cell membranes, is examined. For enzymes embedded in the cell membrane the role of the barrier height (activation energy) is played by the membrane electric potential. This barrier height can be modulated either by internal fluctuations or by external electrical fields, either random or periodic. Existing experimental data on active transport of Na(+) and Rb(+) in human erythrocytes (catalyzed by Na(+)-K(+)-ATPase) can be interpreted as evidence of stochastic resonance between the external ac field and the fluctuations of the membrane potential. The obtained results suggest that the significant part of these fluctuations is supplied by the stimulated action of neighbor voltage-gated ionic channels. This supports the idea that intrinsic noise plays a constructive role in one of most important and most frequent biophysical processs, viz. ion transmission through cell membranes. Means of further experimental verification of this conjecture are proposed. (c) 1998 American Institute of Physics.

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.

Thermodynamics and kinetics of a Brownian motor

Nonequilibrium fluctuations, whether generated externally or by a chemical reaction far from equilibrium, can bias the Brownian motion of a particle in an anisotropic medium without thermal gradients, a net force such as gravity, or a macroscopic electric field. Fluctuation-driven transport is one mechanism by which chemical energy can directly drive the motion of particles and macromolecules and may find application in a wide variety of fields, including particle separation and the design of molecular motors and pumps.

Mechanochemical coupling of the motion of molecular motors to ATP hydrolysis

The typical biochemical paradigm for coupling between hydrolysis of ATP and the performance of chemical or mechanical work involves a well-defined sequence of events (a kinetic mechanism) with a fixed stoichiometry between the number of ATP molecules hydrolyzed and the turnover of the output reaction. Recent experiments show, however, that such a deterministic picture of coupling may not be adequate to explain observed behavior of molecular motor proteins in the presence of applied forces. Here we present a general model in which the binding of ATP and release of ADP serve to modulate the binding energy of a motor protein as it travels along a biopolymer backbone. The mechanism is loosely coupled--the average number of ATPs hydrolyzed to cause a single step from one binding site to the next depends strongly on the magnitude of an applied force and on the effective viscous drag force. The statistical mechanical perspective described here offers insight into how local anisotrophy along the "track" for a molecular motor, combined with an energy-releasing chemical reaction to provide a source of nonequilibrium fluctuations, can lead to macroscopic motion.

Electric parameters of Na+/K(+)-ATPase by measurements of the fluorescence-detected electric dichroism

The electric parameters of Na+/K(+)-ATPase labeled by FITC have been characterized by measurements of the fluorescence-detected electric dichroism. The fluorescence emission was measured with polarizers at the magic angle and the light for excitation was usually polarized parallel to the field vector. The FITC-Na+/K(+)-ATPase preparations exhibit a negative electric dichroism at field strengths up to about 600 V/cm and a positive dichroism at higher field strengths. Pulse reversal experiments reveal a dominant permanent electric moment at low electric field strengths and an increasing contribution from an induced electric moment at higher field strengths. The dichroism rise curves and the transients upon pulse reversal show two relaxation processes with opposite amplitudes, whereas the dichroism decay curves in most cases can be represented by single exponentials at a reasonable accuracy. The amplitude A2 associated with the slower of the rise processes is dominant at low field strengths and also approaches saturation already at low field strengths. The dependence of A2 on the electric field strength is consistent with the orientation function for permanent dipoles and cannot be represented by the orientation function for induced dipoles. The fitted permanent dipole moment is in the range of 3.5 x 10(-24) Cm [1 x 10(6) D] and shows only a relatively small decrease with increasing ionic strength. The stationary values of the electric dichroism up to field strengths E < or = 800 V/cm can be represented with high accuracy by an orientation function for disk-shaped particles with a permanent moment along the particle symmetry axis and an induced moment along the semi-major axis. The permanent electric moment determined according to this function is consistent with the one obtained from the amplitudes A2. In summary, our measurements indicate that Na+/K(+)-ATPase is associated with a large permanent electric moment directed perpendicular to the membrane plane. The dipole moment per ATPase monomer unit is estimated to be 1.4 x 10(-27) Cm [430 +/- 50 D].