A Model for the Long Time-Constant Transient Voltage Response to Current in Epithelial Tissues

Upon passing a step current through the frog gastric mucosa, a transient response in voltage is observed, which can formally be represented by several types of model systems, although some models require elements which are hard to visualize in terms of the known morphology of the mucosa. A physically reasonable model can be constructed by considering the changes in intracellular ionic composition which arise due to current flow, and the consequent changes in diffusion potentials across the two cell membranes. A simple model has been developed which fits the observed long time-constant portion of the transient at low current densities, and predicts departures from exponential behavior at larger currents. Since reasonable values for membrane resistance and cell volume give a fit, it is proposed that this model may account for the long time-constant portion of the transient response. There is no reason to expect that similar considerations do not hold for epithelial tissues in general.     

Adaptation and accommodation in the squid axon

Current clamp data of the squid axon indicate that there is a qualitative change in the adaptive response as the magnitude of the current step is increased. Large stimulus currents have a strong inhibitory effect on spike generation and on active responses in general. Such currents always lead to only one action-potential and to the elimination of post-spike subthreshold oscillation. In view of a direct connection between stimulus current and potassium current I _K, the potassium channel of the Hodgkin-Huxley model is reinterpreted in a natural way such that the K⁺ conductance is directly dependent on I _K in addition to a voltage dependence. The I-_Kdependence seems to dominate whenever the stimulus current is greater than approximately 35 μA/cm². For current ramps, and large current steps, such a current formulation leads to good agreement with the data.     

Functional analysis of human Na~+/K~+-ATPase familial or sporadic hemiplegic migraine mutations expressed in Xenopus oocytes

AIM: Functional characterization of ATP1A2 mutations that are related to familial or sporadic hemiplegic migraine(FHM2, SHM). METHODS: cRNA of human Na+/K+-ATPase α2- and β1-subunits were injected in Xenopus laevis oocytes. FHM2 or SHM mutations of residues located in putative α/β interaction sites or in the α2-subunit's C-terminal region were investigated. Mutants were analyzed by the twoelectrode voltage-clamp(TEVC) technique on Xenopus oocytes. Stationary K+-induced Na+/K+ pump currents were measured, and the voltage dependence of apparent K+ affinity was investigated. Transient currents were recorded as ouabain-sensitive currents in Na+ buffers to analyze kinetics and voltage-dependent presteady state charge translocations. The expression of constructs was verified by preparation of plasma membrane and total membrane fractions of cRNA-injected oocytes. RESULTS: Compared to the wild-type enzyme, the mutants G900R and E902K showed no significant dif-ferences in the voltage dependence of K+-induced currents, and analysis of the transient currents indicated that the extracellular Na+ affinity was not affected. Mutant G855R showed no pump activity detectable by TEVC. Also for L994del and Y1009X, pump currents could not be recorded. Analysis of the plasma and total membrane fractions showed that the expressed proteins were not or only minimally targeted to the plasma membrane. Whereas the mutation K1003E had no impact on K+ interaction, D999H affected the voltage dependence of K+-induced currents. Furthermore, kinetics of the transient currents was altered compared to the wild-type enzyme, and the apparent affinity for extracellular Na+ was reduced. CONCLUSION: The investigated FHM2/SHM mutations influence protein function differently depending on the structural impact of the mutated residue.     

The kinetics of stomatal responses to VPD in Vicia faba: electrophysiological and water relations models

Abstract. An Ohm's law analogy is frequently employed to calculate parameters of leaf gas exchange. For example, resistance to water vapour loss is calculated as the quotient of vapour pressure difference (VPD) and vapour loss by transpiration. In the present research, this electrical analogy was extended. Steady-state transpiration as a function of VPD, assayed in leaflets of Vicia faba using gas exchange techniques, was compared with steady-state K⁺ current magnitude as a function of voltage in isolated guard cell protoplasts of Vicia faba, assayed using the patch clamping technique in the whole cell configuration. An electrophysiological model originally developed to explain the kinetics of current changes following step changes in voltage across a cell membrane was used to fit the kinetics of transpiration changes following step changes in VPD applied to leaflets of Vicia faba. Following step increases in VPD, transpiration exhibited an initial increase, reflecting the increased driving force for water loss and, for large step increases in VPD, a transient decrease in stomatal resistance. Transpiration subsequently declined, reflecting stomatal closure. By analogy to electrophysiological responses, it is hypothesized that the humidity parameter that is sensed by guard cells is VPD. Two models based on epidermal water relations were also applied to transpiration kinetics. In the first model, the transient increase in transpiration following a step increase in VPD was attributed partially to an increase in the Physical driving force (VPD) and partially to a transient decrease in stomatal resistance resulting from reduced epidermal backpressure. In the second model, the transient decrease in stomatal resistance was attributed to a direct response of the guard cells to VPD. Both models based on water relations gave good fits of the data, emphasizing the need for further study regarding the metabolic nature of the guard cell response to humidity.     

Evidence for frequency-dependent extracellular impedance from the transfer function between extracellular and intracellular potentials

Dopaminergic (DA) neurons of the mammalian midbrain exhibit unusually low firing frequencies in vitro. Furthermore, injection of depolarizing current induces depolarization block before high frequencies are achieved. The maximum steady and transient rates are about 10 and 20 Hz, respectively, despite the ability of these neurons to generate bursts at higher frequencies in vivo. We use a three-compartment model calibrated to reproduce DA neuron responses to several pharmacological manipulations to uncover mechanisms of frequency limitation. The model exhibits a slow oscillatory potential (SOP) dependent on the interplay between the L-type Ca²⁺ current and the small conductance K⁺ (SK) current that is unmasked by fast Na⁺ current block. Contrary to previous theoretical work, the SOP does not pace the steady spiking frequency in our model. The main currents that determine the spontaneous firing frequency are the subthreshold L-type Ca²⁺ and the A-type K⁺ currents. The model identifies the channel densities for the fast Na⁺ and the delayed rectifier K⁺ currents as critical parameters limiting the maximal steady frequency evoked by a depolarizing pulse. We hypothesize that the low maximal steady frequencies result from a low safety factor for action potential generation. In the model, the rate of Ca²⁺ accumulation in the distal dendrites controls the transient initial frequency in response to a depolarizing pulse. Similar results are obtained when the same model parameters are used in a multi-compartmental model with a realistic reconstructed morphology, indicating that the salient contributions of the dendritic architecture have been captured by the simpler model.     

Pre-Steady-State Kinetics of Ba-Ca Exchange Reveals a Second Electrogenic Step Involved in Ca Translocation by the Na-Ca Exchanger

Kinetic properties of the Na-Ca exchanger (guinea pig NCX1) expressed in Xenopus oocytes were investigated with excised membrane patches in the inside-out configuration and photolytic Ca²⁺ concentration jumps with either 5 mM extracellular Sr²⁺ or Ba²⁺. After a Ca²⁺ concentration jump on the cytoplasmic side, the exchanger performed Sr-Ca or Ba-Ca exchange. In the Sr-Ca mode, currents are transient and decay in a monoexponential manner similar to that of currents in the Ca-Ca exchange mode described before. Currents recorded in the Ba-Ca mode are also transient, but the decay is biphasic. In the Sr-Ca mode the amount of charge translocated increases at negative potentials in agreement with experiments performed in the Ca-Ca mode. In the Ba-Ca mode the total amount of charge translocated after a Ca²⁺ concentration jump is ∼4 to 5 times that in Ca-Ca or Sr-Ca mode. In the Ba-Ca mode the voltage dependence of charge translocation depends on the Ca²⁺ concentration on the cytosolic side before the Ca²⁺ concentration jump. At low initial Ca²⁺ levels (∼0.5 μM), charge translocation is voltage independent. At a higher initial concentration (1 μM Ca²⁺), the amount of charge translocated increases at positive potentials. Biphasic relaxation of the current was also observed in the Ca-Ca mode if the external Ca²⁺ concentration was reduced to ≤0.5 mM. The results reported here and in previous publications can be described by using a 6-state model with two voltage-dependent conformational transitions.     

A Tight-Seal Whole Cell Study of the Voltage-Dependent Gating Mechanism of K-Channels of Protoplasmic Droplets of Chara corallina

The biophysical properties of voltage-dependent K⁺-channels of protoplasmic droplets of Chara corallina Klein ex Willd., em, R.D.W. were investigated using the tight-seal whole cell method. Two potassium currents were observed in voltage-clamp mode and they can be used to explain the transient membrane potential time course observed in current-clamp mode. The K⁺-channels are identified by the effect of tetraethylammonium chloride which blocks both currents. A two-state, constant dipole moment model is used to fit the voltage-conductance curve. From this model the minimum equivalent gating charge involved in the gating mechanism of K⁺-channels of Chara can be estimated.     

Intrinsic Voltage Dependence and Ca2+ Regulation of mslo Large Conductance Ca-activated K+ Channels

The kinetic and steady-state properties of macroscopic mslo Ca-activated K⁺ currents were studied in excised patches from Xenopus oocytes. In response to voltage steps, the timecourse of both activation and deactivation, but for a brief delay in activation, could be approximated by a single exponential function over a wide range of voltages and internal Ca²⁺ concentrations ([Ca]_i). Activation rates increased with voltage and with [Ca]_i, and approached saturation at high [Ca]_i. Deactivation rates generally decreased with [Ca]_i and voltage, and approached saturation at high [Ca]_i. Plots of the macroscopic conductance as a function of voltage (G-V) and the time constant of activation and deactivation shifted leftward along the voltage axis with increasing [Ca]_i. G-V relations could be approximated by a Boltzmann function with an equivalent gating charge which ranged between 1.1 and 1.8 e as [Ca]_i varied between 0.84 and 1,000 μM. Hill analysis indicates that at least three Ca²⁺ binding sites can contribute to channel activation. Three lines of evidence indicate that there is at least one voltage-dependent unimolecular conformational change associated with mslo gating that is separate from Ca²⁺ binding. (a) The position of the mslo G-V relation does not vary logarithmically with [Ca]_i. (b) The macroscopic rate constant of activation approaches saturation at high [Ca]_i but remains voltage dependent. (c) With strong depolarizations mslo currents can be nearly maximally activated without binding Ca²⁺. These results can be understood in terms of a channel which must undergo a central voltage-dependent rate limiting conformational change in order to move from closed to open, with rapid Ca²⁺ binding to both open and closed states modulating this central step.     

Studies on adenyl cyclase in Necturus gastric mucosa

Adenyl cyclase activity of Necturus gastric mucosa was determined by measuring the amount of radioactive adenosine 3′,5′-cyclic monophosphate formed from ³H-labeled adenosine triphosphate. Histamine, pentagastrin, and fluoride added in vitro significantly increased fundic adenyl cyclase activity. The dose response curves show that the affinity of pentagastrin for adenyl cyclase is greater than that of histamine, whereas the peak response to pentagastrin is less than that to histamine. Additive stimulation was not obtained when maximal doses of pentagastrin and histamine were combined. These findings suggest that gastric mucosa contains a single adenyl cyclase unit which is coupled to distinctive selectivity sites for gastrin and histamine. N-Benzyl-3-pyrrolidyl acetate methobromide (AHR-602), the muscarinic compound, caused a significant reduction in adenyl cyclase activity, indicating a different mechanism of stimulation of gastric acid secretion for cholinergic muscarinic compounds.     

Modeling the Cellular Mechanisms and Olfactory Input Underlying the Triphasic Response of Moth Pheromone-Sensitive Projection Neurons

In the antennal lobe of the noctuid moth Agrotis ipsilon, most pheromone-sensitive projection neurons (PNs) exhibit a triphasic firing pattern of excitation (E₁)-inhibition (I)-excitation (E₂) in response to a pulse of the sex pheromone. To understand the mechanisms underlying this stereotypical discharge, we developed a biophysical model of a PN receiving inputs from olfactory receptor neurons (ORNs) via nicotinic cholinergic synapses. The ORN is modeled as an inhomogeneous Poisson process whose firing rate is a function of time and is fitted to extracellular data recorded in response to pheromone stimulations at various concentrations and durations. The PN model is based on the Hodgkin-Huxley formalism with realistic ionic currents whose parameters were derived from previous studies. Simulations revealed that the inhibitory phase I can be produced by a SK current (Ca²⁺-gated small conductance K⁺ current) and that the excitatory phase E₂ can result from the long-lasting response of the ORNs. Parameter analysis further revealed that the ending time of E₁ depends on some parameters of SK, Ca²⁺, nACh and Na⁺ currents; I duration mainly depends on the time constant of intracellular Ca²⁺ dynamics, conductance of Ca²⁺ currents and some parameters of nACh currents; The mean firing frequency of E₁ and E₂ depends differentially on the interaction of various currents. Thus it is likely that the interplay between PN intrinsic currents and feedforward synaptic currents are sufficient to generate the triphasic firing patterns observed in the noctuid moth A. ipsilon.     

The role of linear and voltage-dependent ionic currents in the generation of slow wave oscillations

Neuronal oscillatory activity is generated by a combination of ionic currents, including at least one inward regenerative current that brings the cell towards depolarized voltages and one outward current that repolarizes the cell. Such currents have traditionally been assumed to require voltage-dependence. Here we test the hypothesis that the voltage dependence of the regenerative inward current is not necessary for generating oscillations. Instead, a current I _NL that is linear in the biological voltage range and has negative conductance is sufficient to produce regenerative activity. The current I _NL can be considered a linear approximation to the negative-conductance region of the current–voltage relationship of a regenerative inward current. Using a simple conductance-based model, we show that I _NL , in conjunction with a voltage-gated, non-inactivating outward current, can generate oscillatory activity. We use phase-plane and bifurcation analyses to uncover a rich variety of behaviors as the conductance of I _NL is varied, and show that oscillations emerge as a result of destabilization of the resting state of the model neuron. The model shows the need for well-defined relationships between the inward and outward current conductances, as well as their reversal potentials, in order to produce stable oscillatory activity. Our analysis predicts that a hyperpolarization-activated inward current can play a role in stabilizing oscillatory activity by preventing swings to very negative voltages, which is consistent with what is recorded in biological neurons in general. We confirm this prediction of the model experimentally in neurons from the crab stomatogastric ganglion.     

Electrophysiological Evidence for Intrinsic Pacemaker Currents in Crayfish Parasol Cells

I used sharp intracellular electrodes to record from parasol cells in the semi-isolated crayfish brain to investigate pacemaker currents. Evidence for the presence of the hyperpolarization-activated inward rectifier potassium current was obtained in about half of the parasol cells examined, where strong, prolonged hyperpolarizing currents generated a slowly-rising voltage sag, and a post-hyperpolarization rebound. The amplitudes of both the sag voltage and the depolarizing rebound were dependent upon the strength of the hyperpolarizing current. The voltage sag showed a definite threshold and was non-inactivating. The voltage sag and rebound depolarization evoked by hyperpolarization were blocked by the presence of 5–10 mM Cs²⁺ ions, 10 mM tetraethyl ammonium chloride, and 10 mM cobalt chloride in the bathing medium, but not by the drug ZD 7288. Cs⁺ ions in normal saline in some cells caused a slight increase in mean resting potential and a reduction in spontaneous burst frequency. Many of the neurons expressing the hyperpolarization-activated inward potassium current also provided evidence for the presence of the transient potassium current I_A, which was inferred from experimental observations of an increased latency of post-hyperpolarization response to a depolarizing step, compared to the response latency to the depolarization alone. The latency increase was reduced in the presence of 4-aminopyridine (4-AP), a specific blocker of I_A. The presence of 4-AP in normal saline also induced spontaneous bursting in parasol cells. It is conjectured that, under normal physiological conditions, these two potassium currents help to regulate burst generation in parasol cells, respectively, by helping to maintain the resting membrane potential near a threshold level for burst generation, and by regulating the rate of rise of membrane depolarizing events leading to burst generation. The presence of post-burst hyperpolarization may depend upon I_A channels in parasol cells.     

An analytical model of memristors in plants

The memristor, a resistor with memory, was postulated by Chua in 1971 and the first solid-state memristor was built in 2008. Recently, we found memristors in vivo in plants. Here we propose a simple analytical model of 2 types of memristors that can be found within plants. The electrostimulation of plants by bipolar periodic waves induces electrical responses in the Aloe vera and Mimosa pudica with fingerprints of memristors. Memristive properties of the Aloe vera and Mimosa pudica are linked to the properties of voltage gated K⁺ ion channels. The potassium channel blocker TEACl transform plant memristors to conventional resistors. The analytical model of a memristor with a capacitor connected in parallel exhibits different characteristic behavior at low and high frequency of applied voltage, which is the same as experimental data obtained by cyclic voltammetry in vivo.     

The effects of Al on the calcium currents inHelix neurons

Summary 1. The effects of aluminium (Al) on calcium (Ca) currents were investigated by using the conventional two-electrode voltage clamp technique inHelix pomatia neurons. The peak amplitude, kinetics, and voltage dependence of activation and inactivation of the Ca currents were studied in the presence of 10^–5–10^–3 M AlCl₃, at pH 6.2. Al prolonged the rising phase of the Ca currents and therefore increased the time to peak at each command voltage step used.3. There was no significant influence of Al on the peak amplitude of the Ca currents, but the voltage dependence of the time to peak, activation, and inactivation of the Ca currents shifted to more positive potentials as a consequence of Al treatment.4. The leak currents were not influenced by Al up to 1 mM, which was the maximal dose applied.5. The results support the suggestion that Al may modify the Ca homeostasis and that it exerts a neurotoxic effect, at least in part, by modulation of the Ca current of the neuronal membrane.     

Proton conductance of cell membranes

Several workers have suggested that cell membranes have a high proton conductance. Our interest in this concept arose from the possibility that the nutrient (submucosal-facing) membrane of the gastric mucosa may have a high proton or hydroxyl ion conductance which would play a role in the regulation of the acid-base balance of the cell. We found that wide changes in the H⁺ concentration of the fluid bathing the nutrient side of the in vitro frog gastric mucosa did not result in significant changes in p.d. However, a maintained change of the H⁺ concentration of the bathing fluid would be expected to produce only a temporary change in p.d. Since a diffusion barrier is present on the nutrient side the temporary change in p.d. might be masked. An analysis of this possibility was made on the basis of a conceptual model and as a result of the analysis it is concluded that the proton (and/or OH^?) conductance of the nutrient membrane of the frog gastric mucosa is not a significant fraction of its total conductance. The present status of the proton conductance hypothesis with respect to striated muscle and to the secretory membrane of the gastric mucosa is reviewed.     

High Ca2+ permeability of a peptide-gated DEG/ENaC from Hydra

Degenerin/epithelial Na⁺ channels (DEG/ENaCs) are Na⁺ channels that are blocked by the diuretic amiloride. In general, they are impermeable for Ca²⁺ or have a very low permeability for Ca²⁺. We describe here, however, that a DEG/ENaC from the cnidarian Hydra magnipapillata, the Hydra Na⁺ channel (HyNaC), is highly permeable for Ca²⁺ (P_Ca/P_Na = 3.8). HyNaC is directly gated by Hydra neuropeptides, and in Xenopus laevis oocytes expressing HyNaCs, RFamides elicit currents with biphasic kinetics, with a fast transient component and a slower sustained component. Although it was previously reported that the sustained component is unselective for monovalent cations, the selectivity of the transient component had remained unknown. Here, we show that the transient current component arises from secondary activation of the Ca²⁺-activated Cl⁻ channel (CaCC) of Xenopus oocytes. Inhibiting the activation of the CaCC leads to a simple on–off response of peptide-activated currents with no apparent desensitization. In addition, we identify a conserved ring of negative charges at the outer entrance of the HyNaC pore that is crucial for the high Ca²⁺ permeability, presumably by attracting divalent cations to the pore. At more positive membrane potentials, the binding of Ca²⁺ to the ring of negative charges increasingly blocks HyNaC currents. Thus, HyNaC is the first member of the DEG/ENaC gene family with a high Ca²⁺ permeability.     

Voltage Clamp of Cardiac Muscle in a Double Sucrose Gap: A Feasibility Study

A method of stabilizing the membrane potential of a small area of cardiac muscle membrane and the limitations of this method are described. Tiny bundles or strands, approximately 80 μm in diameter, of electrically interconnected fibers from the ventricles of rabbit hearts were used in a double sucrose gap. Current records associated with step changes in voltage were complicated by two capacitive surges of current of nodal and nonnodal origin and large “leakage” currents of nonnodal origin resulting mainly from the multifibered nature of the preparation and emphasized by the method. The transient, inward membrane currents in response to moderate depolarizing steps in command potential had the same duration as the upstroke of the action potential. In good runs, currents were smooth and free from notches. These initial currents behaved qualitatively like the initial sodium currents in squid axon and in other excitable membranes. A fraction of the initial sodium current persisted at least as long as 300 ms. The relationship between peak initial current and voltage was graded and linear in the positive direction. In the negative region the relationship was often very steep, indicating insufficient voltage control of all the membranes despite the squareness of the voltage record. Other indications of inadequacy of control could occur and thus even with this optimum preparation of cardiac muscle it was not feasible to analyze quantitatively either the initial or the prolonged sodium currents.     

Platelet adhesive dynamics. Part II: high shear-induced transient aggregation via GPIbalpha-vWF-GPIbalpha bridging

A three-dimensional multiscale computational model, platelet adhesive dynamics (PAD), is developed and applied in Part I and Part II articles to characterize and quantify key biophysical aspects of GPIbα-von-Willebrand-factor (vWF)-mediated interplatelet binding at high shear rates, a necessary and enabling step that initiates shear-induced platelet aggregation. In this article, an adhesive dynamics model of the transient aggregation of two unactivated platelets via GPIbα-vWF-GPIbα bridging is developed and integrated with the three-dimensional hydrodynamic flow model discussed in Part I. Platelet binding efficiencies predicted by PAD are in good agreement with platelet aggregation behavior observed experimentally, as documented in the literature. Deviations from average vWF ligand size or healthy GPIbα-vWF-A1 binding kinetics are observed in simulations to have significant effects on the dynamics of transient platelet aggregation, i.e., the efficiency of platelet aggregation and characteristics of bond failure, in ways that typify diseased conditions. The GPIbα-vWF-A1 bond formation rate is predicted to have piecewise linear dependence on the prevailing fluid shear rate, with a sharp transition in fluid shear dependency at 7200 s⁻¹. Interplatelet bond force-loading is found to be complex and highly nonlinear. These results demonstrate PAD as a powerful predictive modeling tool for elucidating platelet adhesive phenomena under flow.     

Moderate Hypoxia Influences Potassium Outward Currents in Adipose-Derived Stem Cells

Moderate hypoxic preconditioning of adipose-derived stem cells (ASCs) enhances properties such as proliferation and secretion of growth factors, representing a valuable strategy to increase the efficiency of cell-based therapies. In a wide variety of cells potassium (K⁺) channels are key elements involved in the cellular responses to hypoxia, suggesting that ASCs cultured under low oxygen conditions may display altered electrophysiological properties. Here, the effects of moderate hypoxic culture on proliferation, whole-cell currents, and ion channel expression were investigated using human ASCs cultured at 5% and 20% oxygen. Although cell proliferation was greatly enhanced, the dose-dependent growth inhibition by the K⁺ channel blocker tetraethylammonium (TEA) was not significantly affected by hypoxia. Under both normoxic and hypoxic conditions, ASCs displayed outward K⁺ currents composed by Ca²⁺-activated, delayed rectifier, and transient components. Hypoxic culture reduced the slope of the current-voltage curves and caused a negative shift in the voltage activation threshold of the whole-cell currents. However, the TEA-mediated shift of voltage activation threshold was not affected by hypoxia. Semiquantitative real-time RT-PCR revealed that expression of genes encoding for various ion channels subunits related to oxygen sensing and proliferation remained unchanged after hypoxic culture. In conclusion, outward currents are influenced by moderate hypoxia in ASCs through a mechanism that is not likely the result of modulation of TEA-sensitive K⁺ channels.