Active transport of cations in giant axons from Sepia and Loligo

The Na+,K+-ATPase and its stoichiometric ratio: some thermodynamic speculations

 Almost seventy years after its discovery, the sodium-potassium adenosine triphosphatase (the sodium pump) located in the cell plasma membrane remains a source of novel mechanistic and physiologic findings. A noteworthy feature of this enzyme/transporter is its robust stoichiometric ratio under physiological conditions: it sequentially counter-transports three sodium ions and two potassium ions against their electrochemical potential gradients per each hydrolyzed ATP molecule. Here we summarize some present knowledge about the sodium pump and its physiological roles, and speculate whether energetic constraints may have played a role in the evolutionary selection of its characteristic stoichiometric ratio.

Temperature-dependent RNA editing in octopus extensively recodes the neural proteome

In poikilotherms, temperature changes challenge the integration of physiological function. Within the complex nervous systems of the behaviorally sophisticated coleoid cephalopods, these problems are substantial. RNA editing by adenosine deamination is a well-positioned mechanism for environmental acclimation. We report that the neural proteome of Octopus bimaculoides undergoes massive reconfigurations via RNA editing following a temperature challenge. Over 13,000 codons are affected, and many alter proteins that are vital for neural processes. For two highly temperature-sensitive examples, recoding tunes protein function. For synaptotagmin, a key component of Ca2+-dependent neurotransmitter release, crystal structures and supporting experiments show that editing alters Ca2+ binding. For kinesin-1, a motor protein driving axonal transport, editing regulates transport velocity down microtubules. Seasonal sampling of wild-caught specimens indicates that temperature-dependent editing occurs in the field as well. These data show that A-to-I editing tunes neurophysiological function in response to temperature in octopus and most likely other coleoids.

The cellular pathways that maintain the quality control and transport of diverse potassium channels

Potassium channels are multi-subunit transmembrane proteins that permit the selective passage of potassium and play fundamental roles in physiological processes, such as action potentials in the nervous system and organismal salt and water homeostasis, which is mediated by the kidney. Like all ion channels, newly translated potassium channels enter the endoplasmic reticulum (ER) and undergo the error-prone process of acquiring post-translational modifications, folding into their native conformations, assembling with other subunits, and trafficking through the secretory pathway to reach their final destinations, most commonly the plasma membrane. Disruptions in these processes can result in detrimental consequences, including various human diseases. Thus, multiple quality control checkpoints evolved to guide potassium channels through the secretory pathway and clear potentially toxic, aggregation-prone misfolded species. We will summarize current knowledge on the mechanisms underlying potassium channel quality control in the secretory pathway, highlight diseases associated with channel misfolding, and suggest potential therapeutic routes.

Activity-Dependent Fluctuations in Interstitial [K+]: Investigations Using Ion-Sensitive Microelectrodes

In the course of action potential firing, all axons and neurons release K⁺ from the intra- cellular compartment into the interstitial space to counteract the depolarizing effect of Na⁺ influx, which restores the resting membrane potential. This efflux of K⁺ from axons results in K⁺ accumulation in the interstitial space, causing depolarization of the K⁺ reversal potential (E_K), which can prevent subsequent action potentials. To ensure optimal neuronal function, the K⁺ is buffered by astrocytes, an energy-dependent process, which acts as a sink for interstitial K⁺, absorbing it at regions of high concentration and distributing it through the syncytium for release in distant regions. Pathological processes in which energy production is compromised, such as anoxia, ischemia, epilepsy and spreading depression, can lead to excessive interstitial K⁺ accumulation, disrupting sensitive trans-membrane ion gradients and attenuating neuronal activity. The changes that occur in interstitial [K⁺] resulting from both physiological and pathological processes can be monitored accurately in real time using K⁺-sensitive microelectrodes, an invaluable tool in electrophysiological studies.

Effects of In Vivo Intracellular ATP Modulation on Neocortical Extracellular Potassium Concentration

Neuronal and glial activity are dependent on the efflux of potassium ions into the extracellular space. Efflux of K is partly energy-dependent as the activity of pumps and channels which are involved in K transportation is ATP-dependent. In this study, we investigated the effect of decreased intracellular ATP concentration ([ATP]i) on the extracellular potassium ion concentration ([K]o). Using in vivo electrophysiological techniques, we measured neocortical [K]o and the local field potential (LFP) while [ATP]i was reduced through various pharmacological interventions. We observed that reducing [ATP]i led to raised [K]o and DC-shifts resembling spreading depolarization-like events. We proposed that most likely, the increased [K]o is mainly due to the impairment of the Na/K ATPase pump and the ATP-sensitive potassium channel in the absence of sufficient ATP, because Na/K ATPase inhibition led to increased [K]o and ATP-sensitive potassium channel impairment resulted in decreased [K]o. Therefore, an important consequence of decreased [ATP]i is an increased [K]o. The results of this study acknowledge one of the mechanisms involved in [K]o dynamics.

Study of transmembrane ion transport under tonicity imbalance using a combination of low frequency-electrical impedance spectroscopy (LF-EIS) and improved ion transport model

Transmembrane ion transport under tonicity imbalance has been investigated using a combination of low frequency-electrical impedance spectroscopy (LF-EIS) and improved ion transport model, by considering the cell diameterd[m] and the initial intracellular ion concentrationc_in[mM] as a function of tonicity expressed by sucrose concentrationc_s[mM]. The transmembrane ion transport is influenced by extracellular tonicity conditions, leading to a facilitation/inhibition of ion passage through the cell membrane. The transmembrane transport coefficientP[m s^-1], which represents the ability of transmembrane ion transport, is calculated by the extracellular ion concentrations obtained by improved ion transport model and LF-EIS measurement.Pis calculated as 4.11 × 10^-6and 3.44 × 10^-6m s^-1atc_sof 10 and 30 mM representing hypotonic condition, 2.44 × 10^-6m s^-1atc_sof 50 mM representing isotonic condition, and 3.68 × 10^-6, 5.16 × 10^-6, 9.51 × 10^-6, and 14.89 × 10^-6m s^-1atc_sof 75, 100, 125 and 150 mM representing hypertonic condition. The LF-EIS results indicate that the transmembrane ion transport is promoted under hypertonic and hypotonic conditions compared to isotonic condition. To verify the LF-EIS results, fluorescence intensityF[-] of extracellular potassium ions is observed to obtain the temporal distribution of average potassium ion concentration within the region of 3.6μm from cell membrane interfacec_ROI[mM]. The slopes of ∆c_ROI/c_ROI1to timetare 0.0003, 0.0002, and 0.0006 under hypotonic, isotonic, and hypertonic conditions, wherec_ROI1denotes initialc_ROI, which shows the same tendency with LF-EIS result that is verified by the potassium ion fluorescence observation.

Measuring enzyme activities in crude homogenates: Na+/K+-ATPase as a case study in optimizing assays

In this review of assays of Na⁺/K⁺-ATPase (NKA), we explore the choices made by researchers assaying the enzyme to investigate its role in physiological regulation. We survey NKA structure and function in the context of how it is typically assayed, and how technical choices influence what can be said about the enzyme. In comparing different methods for extraction and assay of NKA, we identified a series of common pitfalls that compromise the veracity of results. We include experimental work to directly demonstrate how choices in detergents, salts and substrates influence NKA activities measured in crude homogenates. Our review of assay approaches integrates what is known from enzymology, biomedical physiology, cell biology and evolutionary biology, offering a more robust method for assaying the enzyme in meaningful ways, identifying caveats and future directions to explore its structure and function. The goal is to provide the sort of background on the enzyme that should be considered in exploring the function of the enzyme in comparative physiology.

The role of AMPK in regulation of Na+,K+-ATPase in skeletal muscle: does the gauge always plug the sink?

AMP-activated protein kinase (AMPK) is a cellular energy gauge and a major regulator of cellular energy homeostasis. Once activated, AMPK stimulates nutrient uptake and the ATP-producing catabolic pathways, while it suppresses the ATP-consuming anabolic pathways, thus helping to maintain the cellular energy balance under energy-deprived conditions. As much as ~ 20-25% of the whole-body ATP consumption occurs due to a reaction catalysed by Na⁺,K⁺-ATPase (NKA). Being the single most important sink of energy, NKA might seem to be an essential target of the AMPK-mediated energy saving measures, yet NKA is vital for maintenance of transmembrane Na⁺ and K⁺ gradients, water homeostasis, cellular excitability, and the Na⁺-coupled transport of nutrients and ions. Consistent with the model that AMPK regulates ATP consumption by NKA, activation of AMPK in the lung alveolar cells stimulates endocytosis of NKA, thus suppressing the transepithelial ion transport and the absorption of the alveolar fluid. In skeletal muscles, contractions activate NKA, which opposes a rundown of transmembrane ion gradients, as well as AMPK, which plays an important role in adaptations to exercise. Inhibition of NKA in contracting skeletal muscle accentuates perturbations in ion concentrations and accelerates development of fatigue. However, different models suggest that AMPK does not inhibit or even stimulates NKA in skeletal muscle, which appears to contradict the idea that AMPK maintains the cellular energy balance by always suppressing ATP-consuming processes. In this short review, we examine the role of AMPK in regulation of NKA in skeletal muscle and discuss the apparent paradox of AMPK-stimulated ATP consumption.

How is information transmitted in a nerve?

In the last 15 years, a debate has emerged about the validity of the famous Hodgkin-Huxley model for nerve impulse. Mechanical models have been proposed. This note reviews the experimental properties of the nerve impulse and discusses the proposed alternatives. The experimental data, which rule out some of the alternative suggestions, show that while the Hodgkin-Huxley model may not be complete, it nevertheless includes essential features that should not be overlooked in the attempts made to improve, or supersede, it.

Multipurpose Na+ ions mediate excitation and cellular homeostasis: Evolution of the concept of Na+ pumps and Na+/Ca2+ exchangers

Ionic signalling is the most ancient form of regulation of cellular functions in response to environmental challenges. Signals, mediated by Na⁺ fluxes and spatio-temporal fluctuations of Na⁺ concentration in cellular organelles and cellular compartments contribute to the most fundamental cellular processes such as membrane excitability and energy production. At the very core of ionic signalling lies the Na⁺-K⁺ ATP-driven pump (or NKA) which creates trans-plasmalemmal ion gradients that sustain ionic fluxes through ion channels and numerous Na⁺-dependent transporters that maintain cellular and tissue homeostasis. Here we present a brief account of the history of research into NKA, Na⁺ -dependent transporters and Na⁺ signalling.

Conformational changes upon gating of KirBac1.1 into an open-activated state revealed by solid-state NMR and functional assays

Inward rectifier K⁺ (Kir) channels play an important role in reestablishing the resting membrane state of the action potential of excitable cells in humans. KirBac1.1 is a prokaryotic Kir channel with a high degree of homology to human Kir channels and can be isotopically labeled in NMR quantities for structural studies. Functional assays and NMR assignments confirm that KirBac1.1 is in a constitutively conductive state. Solid-state NMR assignments further reveal alternate conformations at key sites in the protein that are well conserved through human Kir channels, hinting at a possible allosteric network between channels. These underlying sequential and structural motifs could explain abnormal conductive properties of these channels fundamental to their native gating processes.

The conformational changes required for activation and K⁺ conduction in inward-rectifier K⁺ (Kir) channels are still debated. These structural changes are brought about by lipid binding. It is unclear how this process relates to fast gating or if the intracellular and extracellular regions of the protein are coupled. Here, we examine the structural details of KirBac1.1 reconstituted into both POPC and an activating lipid mixture of 3:2 POPC:POPG (wt/wt). KirBac1.1 is a prokaryotic Kir channel that shares homology with human Kir channels. We establish that KirBac1.1 is in a constitutively active state in POPC:POPG bilayers through the use of real-time fluorescence quenching assays and Förster resonance energy transfer (FRET) distance measurements. Multidimensional solid-state NMR (SSNMR) spectroscopy experiments reveal two different conformers within the transmembrane regions of the protein in this activating lipid environment, which are distinct from the conformation of the channel in POPC bilayers. The differences between these three distinct channel states highlight conformational changes associated with an open activation gate and suggest a unique allosteric pathway that ties the selectivity filter to the activation gate through interactions between both transmembrane helices, the turret, selectivity filter loop, and the pore helix. We also identify specific residues involved in this conformational exchange that are highly conserved among human Kir channels.

Stationary and Nonstationary Ion and Water Flux Interactions in Kidney Proximal Tubule: Mathematical Analysis of Isosmotic Transport by a Minimalistic Model

Our mathematical model of epithelial transport (Larsen et al. Acta Physiol. 195:171–186, 2009) is extended by equations for currents and conductance of apical SGLT2. With independent variables of the physiological parameter space, the model reproduces intracellular solute concentrations, ion and water fluxes, and electrophysiology of proximal convoluted tubule. The following were shown:

Cation trafficking propels RNA hydrolysis

Catalysis by members of the RNase H superfamily of enzymes is generally believed to require only two Mg²⁺ ions that are coordinated by active-site carboxylates. By examining the catalytic process of Bacillus halodurans RNase H1 in crystallo, however, we found that the two canonical Mg²⁺ ions and an additional K⁺ failed to align the nucleophilic water for RNA cleavage. Substrate alignment and product formation required a second K⁺ and a third Mg²⁺, which replaced the first K⁺ and departed immediately after cleavage. A third transient Mg²⁺ has also been observed for DNA synthesis, but in that case it coordinates the leaving group instead of the nucleophile as in the case of the RNase H1 hydrolysis reaction. These transient cations have no contact with the enzymes. Other DNA and RNA enzymes that catalyze consecutive cleavage and strand-transfer reactions in a single active site may similarly require cation trafficking coordinated by the substrate.

Unraveling Synaptic GCaMP Signals: Differential Excitability and Clearance Mechanisms Underlying Distinct Ca2+ Dynamics in Tonic and Phasic Excitatory, and Aminergic Modulatory Motor Terminals in Drosophila

GCaMP is an optogenetic Ca²⁺ sensor widely used for monitoring neuronal activities but the precise physiological implications of GCaMP signals remain to be further delineated among functionally distinct synapses. The Drosophila neuromuscular junction (NMJ), a powerful genetic system for studying synaptic function and plasticity, consists of tonic and phasic glutamatergic and modulatory aminergic motor terminals of distinct properties. We report a first simultaneous imaging and electric recording study to directly contrast the frequency characteristics of GCaMP signals of the three synapses for physiological implications. Different GCaMP variants were applied in genetic and pharmacological perturbation experiments to examine the Ca²⁺ influx and clearance processes underlying the GCaMP signal. Distinct mutational and drug effects on GCaMP signals indicate differential roles of Na⁺ and K⁺ channels, encoded by genes including paralytic (para), Shaker (Sh), Shab, and ether-a-go-go (eag), in excitability control of different motor terminals. Moreover, the Ca²⁺ handling properties reflected by the characteristic frequency dependence of the synaptic GCaMP signals were determined to a large extent by differential capacity of mitochondria-powered Ca²⁺ clearance mechanisms. Simultaneous focal recordings of synaptic activities further revealed that GCaMPs were ineffective in tracking the rapid dynamics of Ca²⁺ influx that triggers transmitter release, especially during low-frequency activities, but more adequately reflected cytosolic residual Ca²⁺ accumulation, a major factor governing activity-dependent synaptic plasticity. These results highlight the vast range of GCaMP response patterns in functionally distinct synaptic types and provide relevant information for establishing basic guidelines for the physiological interpretations of presynaptic GCaMP signals from in situ imaging studies.

A Perspective on the Value of Aquatic Models in Biomedical Research

For at least 150 years, biological scientists have congregated at marine laboratories, located at the edge of the sea, to explore aquatic life. The purpose of this minireview is to offer a brief perspective on the relevance of this activity to our knowledge of human physiology and disease, drawing heavily on the experience of the authors and without attempting to offer a comprehensive history of the many contributions of marine models to biomedical research.

ER Stress-Mediated Signaling: Action Potential and Ca(2+) as Key Players

The proper functioning of the endoplasmic reticulum (ER) is crucial for multiple cellular activities and survival. Disturbances in the normal ER functions lead to the accumulation and aggregation of unfolded proteins, which initiates an adaptive response, the unfolded protein response (UPR), in order to regain normal ER functions. Failure to activate the adaptive response initiates the process of programmed cell death or apoptosis. Apoptosis plays an important role in cell elimination, which is essential for embryogenesis, development, and tissue homeostasis. Impaired apoptosis can lead to the development of various pathological conditions, such as neurodegenerative and autoimmune diseases, cancer, or acquired immune deficiency syndrome (AIDS). Calcium (Ca(2+)) is one of the key regulators of cell survival and it can induce ER stress-mediated apoptosis in response to various conditions. Ca(2+) regulates cell death both at the early and late stages of apoptosis. Severe Ca(2+) dysregulation can promote cell death through apoptosis. Action potential, an electrical signal transmitted along the neurons and muscle fibers, is important for conveying information to, from, and within the brain. Upon the initiation of the action potential, increased levels of cytosolic Ca(2+) (depolarization) lead to the activation of the ER stress response involved in the initiation of apoptosis. In this review, we discuss the involvement of Ca(2+) and action potential in ER stress-mediated apoptosis.

Na(+)/K(+) pump interacts with the h-current to control bursting activity in central pattern generator neurons of leeches

The dynamics of different ionic currents shape the bursting activity of neurons and networks that control motor output. Despite being ubiquitous in all animal cells, the contribution of the Na(+)/K(+) pump current to such bursting activity has not been well studied. We used monensin, a Na(+)/H(+) antiporter, to examine the role of the pump on the bursting activity of oscillator heart interneurons in leeches. When we stimulated the pump with monensin, the period of these neurons decreased significantly, an effect that was prevented or reversed when the h-current was blocked by Cs(+). The decreased period could also occur if the pump was inhibited with strophanthidin or K(+)-free saline. Our monensin results were reproduced in model, which explains the pump's contributions to bursting activity based on Na(+) dynamics. Our results indicate that a dynamically oscillating pump current that interacts with the h-current can regulate the bursting activity of neurons and networks.

A Tunable Magnetic Domain Wall Conduit Regulating Nanoparticle Diffusion

We demonstrate a general and robust method to confine on a plane strongly diffusing nanoparticles in water by using size tunable magnetic channels. These virtual conduits are realized with pairs of movable Bloch walls located within an epitaxially grown ferrite garnet film. We show that once inside the magnetic conduit the particles experience an effective local parabolic potential in the transverse direction, while freely diffusing along the conduit. The stiffness of the magnetic potential is determined as a function of field amplitude that varies the width of the magnetic channel. Precise control of the degree of confinement is demonstrated by tuning the applied field. The magnetic conduit is then used to realize single files of nonpassing particles and to induce periodic condensation of an ensemble of particles into parallel stripes in a completely controllable and reversible manner.

A structural rearrangement of the Na+/K+-ATPase traps ouabain within the external ion permeation pathway

With the use of the energy of ATP hydrolysis, the Na+/K+-ATPase is able to transport across the cell membrane Na+ and K+ against their electrochemical gradients. The enzyme is strongly inhibited by ouabain and its derivatives, some that are therapeutically used for patients with heart failure (cardiotonic steroids). Using lanthanide resonance energy transfer, we trace here the conformational changes occurring on the external side of functional Na+/K+-ATPases induced by the binding of ouabain. Changes in donor/acceptor pair distances are mainly observed within the α subunit of the enzyme. To derive a structural model matching the experimental lanthanide resonance energy transfer distances measured with bound ouabain, we carried out molecular dynamics simulations with energy restraints applied simultaneously using a novel methodology with multiple non-interacting fragments. The restrained simulation, initiated from the X-ray structure of the E2(2K+) state, became strikingly similar to the X-ray structure of the sodium-bound state. The final model shows that ouabain is trapped within the external ion permeation pathway of the pump.

Once upon a time the cell membranes: 175 years of cell boundary research

All modern cells are bounded by cell membranes best described by the fluid mosaic model. This statement is so widely accepted by biologists that little attention is generally given to the theoretical importance of cell membranes in describing the cell. This has not always been the case. When the Cell Theory was first formulated in the XIX(th) century, almost nothing was known about the cell membranes. It was not until well into the XX(th) century that the existence of the plasma membrane was broadly accepted and, even then, the fluid mosaic model did not prevail until the 1970s. How were the cell boundaries considered between the articulation of the Cell Theory around 1839 and the formulation of the fluid mosaic model that has described the cell membranes since 1972? In this review I will summarize the major historical discoveries and theories that tackled the existence and structure of membranes and I will analyze how these theories impacted the understanding of the cell. Apart from its purely historical relevance, this account can provide a starting point for considering the theoretical significance of membranes to the definition of the cell and could have implications for research on early life.

Electrical activity and metabolism in cardiac tissue: An experimental and theoretical study

(1) Effects of the metabolic inhibitor 2,4-dinitrophenol (DNP) on electrical activity in frog atria were studied by means of the sucrose-gap technique and in tracer experiments. (2) Voltage-clamp studies of ionic membrane currents showed a suppression by DNP of peak Na inward current without marked changes in the kinetics of the Na-carrying system and an increase of steady state outward current to three to five times its normal value. In(42)K tracer experiments, DNP increased K resting efflux by about 10% and decreased K influx by 25 to 30%. (3) The depression of Na inward current is regarded as being caused by a partial block of Na channels and an increase of internal Na concentration after inhibition of active Na extrusion. (4) The strong rise in outward current is probably not caused by a K current since K efflux fails to show a correspondingly large change. As a possible explanation for current and flux changes, an electrogenic K pump is discussed. (5) A mathematical model of a carrier system transporting a single ion species is described. The system is designed as a direct "potential" pump. Uphill transport requires an asymmetry of the rate constants governing the cyclic formation and breakdown of carrier-ion complex. The asymmetry is brought about by an input of metabolic energy. Reduction of energy input decreases the asymmetry and induces a carrier-mediated downhill ion movement, with corresponding changes in membrane current and ion fluxes. (6) A model of electrogenic K inward transport is calculated that approximately accounts for the steady state current and the K flux changes experimentally observed after inhibition.

Electrical characteristics of the ionic psn-junction as a model of the resting axon membrane

As a model for the resting axon membrane, we propose the ionic psn-junction. Its electrical characteristics can be determined in close analogy to the corresponding electronic semiconductor junction. Using the "semianalytic approximation", we calculated the electrical capacity and the ionic currents. In contrast to the abrupt pn-junction, the electrical capacity of the psn-junction turns out to be practically voltage-independent, as it is observed for the squid axon membrane. The passive ionic fluxes for K(+), Na(+) and Cl(-), as the main contributions to the total charge flux, are calculated and compared with literature data on the ion fluxes through the resting squid axon membrane as measured by use of radioactive tracers. From this comparison, the ionic permeabilities can be evaluated and used to compute the resting membrane conductivity, which is found to be close to the experimental value. Further evidence in favor of the proposed asymmetrical membrane structure and possible ways of its test by the methods of protein chemistry are discussed.

Is cold paresis related to axonal depolarization?

Cold paresis may occur in multifocal motor neuropathy and lower motor neuron disease. It was proposed to reflect nerve lesions where axons are depolarized due to loss of Na/K-pump activity. In those circumstances, a further decrease in pump activity by cooling may induce extra depolarization, conduction block, and weakness. Evidence for this hypothesis is incomplete because it is unknown if cold induces depolarization in human motor axons and other factors may contribute to the symptoms. To solve these questions, we examined 10 normal subjects. At 37, 25, 20, and 15°C we assessed: excitability in the median nerve, decrement on 3-Hz stimulation, pulsed Doppler of a wrist artery, and thenar muscle strength. Cooling induced: (1) findings compatible with axonal depolarization on excitability testing (fanning-in of threshold electrotonus, steepened current threshold relation, increased refractory period, decreased super- and subexcitability), (2) decreased Doppler peak systolic velocity without causing ischemia, (3) decreased muscle strength and impaired muscle relaxation. Decrement tests and compound muscle action potential amplitude remained normal. The excitability findings induced by cooling were best explained by axonal depolarization due to the effect of temperature on Na/K-pump activity. The induced weakness may be explained not only by this mechanism but also by impaired muscle contraction.

Energy variational analysis of ions in water and channels: Field theory for primitive models of complex ionic fluids

Ionic solutions are mixtures of interacting anions and cations. They hardly resemble dilute gases of uncharged noninteracting point particles described in elementary textbooks. Biological and electrochemical solutions have many components that interact strongly as they flow in concentrated environments near electrodes, ion channels, or active sites of enzymes. Interactions in concentrated environments help determine the characteristic properties of electrodes, enzymes, and ion channels. Flows are driven by a combination of electrical and chemical potentials that depend on the charges, concentrations, and sizes of all ions, not just the same type of ion. We use a variational method EnVarA (energy variational analysis) that combines Hamilton's least action and Rayleigh's dissipation principles to create a variational field theory that includes flow, friction, and complex structure with physical boundary conditions. EnVarA optimizes both the action integral functional of classical mechanics and the dissipation functional. These functionals can include entropy and dissipation as well as potential energy. The stationary point of the action is determined with respect to the trajectory of particles. The stationary point of the dissipation is determined with respect to rate functions (such as velocity). Both variations are written in one Eulerian (laboratory) framework. In variational analysis, an "extra layer" of mathematics is used to derive partial differential equations. Energies and dissipations of different components are combined in EnVarA and Euler-Lagrange equations are then derived. These partial differential equations are the unique consequence of the contributions of individual components. The form and parameters of the partial differential equations are determined by algebra without additional physical content or assumptions. The partial differential equations of mixtures automatically combine physical properties of individual (unmixed) components. If a new component is added to the energy or dissipation, the Euler-Lagrange equations change form and interaction terms appear without additional adjustable parameters. EnVarA has previously been used to compute properties of liquid crystals, polymer fluids, and electrorheological fluids containing solid balls and charged oil droplets that fission and fuse. Here we apply EnVarA to the primitive model of electrolytes in which ions are spheres in a frictional dielectric. The resulting Euler-Lagrange equations include electrostatics and diffusion and friction. They are a time dependent generalization of the Poisson-Nernst-Planck equations of semiconductors, electrochemistry, and molecular biophysics. They include the finite diameter of ions. The EnVarA treatment is applied to ions next to a charged wall, where layering is observed. Applied to an ion channel, EnVarA calculates a quick transient pile-up of electric charge, transient and steady flow through the channel, stationary "binding" in the channel, and the eventual accumulation of salts in "unstirred layers" near channels. EnVarA treats electrolytes in a unified way as complex rather than simple fluids. Ad hoc descriptions of interactions and flow have been used in many areas of science to deal with the nonideal properties of electrolytes. It seems likely that the variational treatment can simplify, unify, and perhaps derive and improve those descriptions.

Cold paresis in multifocal motor neuropathy

Increased weakness during cold (cold paresis) was reported in single cases of multifocal motor neuropathy (MMN). This was unexpected because demyelination is a feature of MMN and symptoms of demyelination improve, rather than worsen, in cold. It was hypothesized that cold paresis in MMN does not reflect demyelination only, but may indicate the existence of inflammatory nerve lesions with permanently depolarized axons that only just conduct at normal temperature, but fail at lower temperatures. We investigated symptoms of cold paresis in 50 MMN patients, 48 chronic inflammatory demyelinating polyneuropathy (CIDP) patients, 35 progressive spinal muscular atrophy (PSMA) patients, and 25 chronic idiopathic axonal polyneuropathy patients. We also investigated symptoms of increased weakness during warmth (heat paresis). Cold paresis was reported more often than heat paresis. Cold paresis was most frequently reported in MMN. Multivariate analysis indicated that MMN patients had a 4- to 6-fold higher risk of reporting cold paresis than CIDP or PSMA patients. Because cold paresis is not consistent with demyelination, the lesions in MMN may involve other mechanisms than demyelination only. In conclusion, symptoms of cold paresis are common in peripheral nervous system disorders, particularly in MMN. This supports the above-described hypothesis.

Some properties of the external activation site of the sodium pump in crab nerve

1. Methods are described for using the changes in respiration of intact Libinia nerve to follow the rate of energy utilization by the sodium pump in this tissue.2. Short tetani in 10 K(Na)ASW (artificial sea water in which Na is the major cation and the potassium concentration is 10 mM) increased the oxygen uptake which then declined exponentially. From the net influx of Na during the tetanus and the associated oxygen uptake, values between 1.9 and 3.4 were calculated for the Na: approximately P ratio. After longer tetani, the recovery curve was S-shaped.3. The pump was activated by potassium ions in the external medium and this activation was competitively inhibited by external sodium ions. The data are consistent with a Michaelis constant (K(m)) for external potassium of 1 mM and an inhibitor constant (K(i)) for external sodium of 60 mM.4. In activating the pump, K could be replaced by Tl(+), Rb, NH(4) and Cs ions; but, of the monovalent ions tested, sodium seemed to be unique in its inhibitory action.5. In sea waters containing 460 mM-Na, ouabain behaved like a mixed inhibitor of the pump, reducing both the maximum velocity and the apparent affinity for external potassium. At a given ouabain concentration, reducing the sodium content of the medium was without effect on the maximum rate of pumping; but the apparent affinity for potassium increased more steeply than in a ouabain-free solution.6. The rate of energy utilization associated with pumping was unaffected by inclusion of quite high concentrations of sulphydryl-blocking agents in the external medium.

Diffusion of finite-sized hard-core interacting particles in a one-dimensional box: Tagged particle dynamics

We solve a nonequilibrium statistical-mechanics problem exactly, namely, the single-file dynamics of N hard-core interacting particles (the particles cannot pass each other) of size Delta diffusing in a one-dimensional system of finite length L with reflecting boundaries at the ends. We obtain an exact expression for the conditional probability density function rhoT(yT,t|yT,0) that a tagged particle T (T=1,...,N) is at position yT at time t given that it at time t=0 was at position yT,0. Using a Bethe ansatz we obtain the N -particle probability density function and, by integrating out the coordinates (and averaging over initial positions) of all particles but particle T , we arrive at an exact expression for rhoT(yT,t|yT,0) in terms of Jacobi polynomials or hypergeometric functions. Going beyond previous studies, we consider the asymptotic limit of large N , maintaining L finite, using a nonstandard asymptotic technique. We derive an exact expression for rhoT(yT,t|yT,0) for a tagged particle located roughly in the middle of the system, from which we find that there are three time regimes of interest for finite-sized systems: (A) for times much smaller than the collision time t<<taucoll=1/(rho2D) , where rho=N/L is the particle concentration and D is the diffusion constant for each particle, the tagged particle undergoes a normal diffusion; (B) for times much larger than the collision time t >>taucoll but times smaller than the equilibrium time t<<taueq=L2/D, we find a single-file regime where rhoT(yT,t|yT,0) is a Gaussian with a mean-square displacement scaling as t1/2; and (C) for times longer than the equilibrium time t>>taue , rhoT(yT,t|yT,0) approaches a polynomial-type equilibrium probability density function. Notably, only regimes (A) and (B) are found in the previously considered infinite systems.

Axonal ion channels from bench to bedside: a translational neuroscience perspective

Over recent decades, the development of specialised techniques such as patch clamping and site-directed mutagenesis have established the contribution of neuronal ion channel dysfunction to the pathophysiology of common neurological conditions including epilepsy, multiple sclerosis, spinal cord injury, peripheral neuropathy, episodic ataxia, amyotrophic lateral sclerosis and neuropathic pain. Recently, these insights from in vitro studies have been translated into the clinical realm. In keeping with this progress, novel clinical axonal excitability techniques have been developed to provide information related to the activity of a variety of ion channels, energy-dependent pumps and ion exchange processes activated during impulse conduction in peripheral axons. These non-invasive techniques have been extensively applied to the study of the biophysical properties of human peripheral nerves in vivo and have provided important insights into axonal ion channel function in health and disease. This review will provide a translational perspective, focusing on an overview of the investigational method, the clinical utility in assessing the biophysical basis of ectopic symptom generation in peripheral nerve disease and a review of the major findings of excitability studies in acquired and inherited neurological disease states.

Membrane potential changes associated with tachyphylaxis and potentiation of the response to stimulating drugs in smooth muscle

Conditions which affect the response of smooth muscle to repeated application of stimulating drugs have been investigated. In guinea-pig taenia coli, tension changes were recorded simultaneously with membrane potential changes using the sucrose gap technique. Acetylcholine, histamine, and 5-hydroxytryptamine caused depolarization and, after removal of the drug, hyperpolarization which was followed by a sequence of damped oscillations of the membrane potential. The average rate of depolarization decreased in the order acetylcholine>histamine >5-hydroxytryptamine. The readiness with which tachyphylaxis occurred increased in the order acetylcholine<histamine<5-hydroxytryptamine. When a dose of a stimulating drug was repeated, the response obtained depended on the phase of the oscillatory potential changes during which it was applied. In general the effect was depressed during a phase of polarization and enhanced during a phase of depolarization. The degree of tachyphylaxis-or potentiation-depended not only on the direction in which the membrane potential changed at the moment of drug application, but also on the relation between the rate at which this potential change took place and the rate of depolarization caused by the drug. The results observed are consistent with the hypothesis that the fluctuating excitability and polarization of the smooth muscle membrane is brought about by periodical changes in the rate of active ion transport and other stabilizing processes in the cell membrane which depend on the rate of metabolic energy supply. The muscle was sensitized to acetylcholine and histamine by previous treatment with, or in the presence of, 5-hydroxytryptamine.

A period of convergence in the studies on muscle contraction and relaxation: the Ebashi's contribution

The object of this paper is to trace the growth of a fundamental problem that for a decade hindered the development of several lines of muscle research: the molecular mechanism that allows and controls contraction and relaxation of muscle fiber. Emphasis is placed on the difficulties to be overcome; thus the paper records not only the achievements and successes, but also the unavoidable failure and disappointments. The account highlights the essential contribution of Setsuro Ebashi to find the solution of the problem.

Acute energy restriction triggers Wallerian degeneration in mouse

Acute exposure of peripheral axons to the free radical Nitric Oxide (NO) may trigger conduction block and, if prolonged, Wallerian degeneration. It was hypothesized that this neurotoxic effect of NO may be due primarily to energy restriction by inhibition of mitochondrial respiration. We compared the neurotoxic effect of NO with the effect of the mitochondrial uncoupler 2,4-dinitrophenol (DNP) on electrically active axons of mouse sciatic nerve. The right tibial nerve was stimulated at the ankle. Muscle responses were recorded from plantar muscles and ascending nerve action potentials were recorded form the exposed sciatic nerve by means of a hook electrode. The sciatic nerve was focally immersed over a length of 1 cm in either phosphate buffered saline (PBS), a solution of approximately 4 microM NO obtained from 10 mM of the NO-donor DETA NONOate, or a solution of up to 1 mM DNP. Following 3 hours of 200 Hz stimulation, the nerves were washed in PBS for 1 hour, the surgical wounds were closed and the mice were left to recover. Following repetitive stimulation in PBS, the nerve responses recovered within 1 hour and the muscle responses within 1 day. The effects of focal acute exposure to NO or DNP were similar: (i) a transient conduction failure that rapidly normalized within one hour of washout and (ii) subsequent Wallerian degeneration of some axons confirmed at morphological studies. Taken together, these data support the hypothesis that neurotoxicity may be caused by energy restriction. Since the pharmacologic effect of NO and DNP was only transient, our data suggest that even a brief period of focal energy restriction can trigger Wallerian degeneration.

Structural basis of Na(+)/K(+)-ATPase adaptation to marine environments

Throughout evolution, enzymes have adapted to perform in different environments. The Na(+)/K(+) pump, an enzyme crucial for maintaining ionic gradients across cell membranes, is strongly influenced by the ionic environment. In vertebrates, the pump sees much less external Na(+) (100-160 mM) than it does in osmoconformers such as squid (450 mM), which live in seawater. If the extracellular architecture of the squid pump were identical to that of vertebrates, then at the resting potential, the pump's function would be severely compromised because the negative voltage would drive Na(+) ions back to their binding sites, practically abolishing forward transport. Here we show that four amino acids that ring the external mouth of the ion translocation pathway are more positive in squid, thereby reducing the pump's sensitivity to external Na(+) and explaining how it can perform optimally in the marine environment.

Uremic neuropathy: clinical features and new pathophysiological insights

Neuropathy is a common complication of end-stage kidney disease (ESKD), typically presenting as a distal symmetrical process with greater lower-limb than upper-limb involvement. The condition is of insidious onset, progressing over months. and has been estimated to be present in 60%-100% of patients on dialysis. Neuropathy generally only develops at glomerular filtration rates of less than 12 ml/min. The most frequent clinical features reflect large-fiber involvement, with paresthesias, reduction in deep tendon reflexes, impaired vibration sense, muscle wasting, and weakness. Nerve conduction studies demonstrate findings consistent with a generalized neuropathy of the axonal type. Patients may also develop autonomic features, with postural hypotension, impaired sweating, diarrhea, constipation, or impotence. The development of uremic neuropathy has been related previously to the retention of neurotoxic molecules in the middle molecular range, although this hypothesis lacked formal proof. Studies utilizing novel axonal excitability techniques have recently shed further light on the pathophysiology of this condition. Nerves of uremic patients have been shown to exist in a chronically depolarized state prior to dialysis, with subsequent improvement and normalization of resting membrane potential after dialysis. The degree of depolarization correlates with serum K(+), suggesting that chronic hyperkalemic depolarization plays an important role in the development of nerve dysfunction in ESKD. These recent findings suggest that maintenance of serum K(+) within normal limits between periods of dialysis, rather than simple avoidance of hyperkalemia, is likely to reduce the incidence and severity of uremic neuropathy.