Nonequilibrium voltage fluctuations in biological membranes. II. Voltage and current noise generated by ion carriers, channels and electrogenic pumps

As applications of the general theoretical framework of charge transport in biological membranes and related voltage and current noise, a number of model calculations are presented for ion carriers, rigid channels, channels with conformational substates and electrogenic pumps. The results are discussed with special reference to the problem of threshold values for sensory transduction processes and their limitations by voltage fluctuations. Furthermore, starting from the special results of model calculations, an attempt is made to determine more general aspects of electric fluctuations generated by charge-transport processes in biological membranes: different frequency dependences of voltage and current noise, and dependence of noise intensities with increasing distance from the equilibrium state.     

Nonequilibrium voltage fluctuations in biological membranes. I. General framework of charge transport in discrete systems and related voltage noise

This paper continues our work on the theory of nonequilibrium voltage noise generated by electric transport processes in membranes. Introducing the membrane voltage as a further variable, a system of kinetic equations linearized in voltage is derived by which generally the time-dependent behaviour of charge-transport processes under varying voltage can be discussed. Using these equations, the treatment of voltage noise can be based on the usual master equation approach to steady-state fluctuations of scalar quantities. Thus, a general theoretical approach to nonequilibrium voltage noise is presented, completing our approach to current fluctuations which had been developed some years ago. It is explicitly shown that at equilibrium the approach yields agreement with the Nyquist relation, while at nonequilibrium this relation is not valid. A further general property of voltage noise is the reduction of low-frequency noise with increasing number of transport units as a consequence of the interactions via the electric field. In a second paper, the approach will be applied for a number of special transport mechanisms, such as ionic channels, carriers or electrogenic pumps.     

Ionic current through batrachotoxin-modified sodium channels of the ranvier node membrane at high positive and negative potentials

Ionic current through batrachotoxin (BTX)-modified sodium channels within a wide range of membrane potentials were measured by the voltage clamp method on the membrane of a myelinated frog nerve fiber. At high positive voltages (above +80 mV) the current decreased with time; with an increase in voltage the steady-state level of the currents fell. The results of measurement of "instant" currents showed that this phenomenon is connected with a decrease in overall conductivity of the modified channels. Scorpion toxin had no significant effect on the kinetics of decline of the currents. This indicates that they are due to processes which differ from ordinary inactivation. In the presence of procaine, at high positive voltages slow (tens of milliseconds) potential-dependent blocking of BTX-modified channels was observed. An increase in negative potentials above ?100 mV caused a decrease in "instant" currents, connected with rapid potential-dependent blocking of BTX-modified sodium channels by calcium ions.     

Transport noise in membranes. Current and voltage fluctuations at equilibrium

A formulism is described for the treatment of noise resulting from the transport of ions in channels containing an arbitrary number of activation energy barriers. The analysis is based on Nyquist's theorem and is therefore restricted to fluctuations around the equilibrium state. Within this limit the spectral intensities of current and voltage noise are given by the frequency-dependent admittance, which in turn is closely linked to the relaxation-time spectrum of the transport system. Explicit expressions for the spectral intensity of current noise are derived for channels with two and three energy barriers. The analysis may be used to predict the spectral intensity of noise from the gating system in nerve.     

Comparison of excitatory currents activated by different transmitters on crustacean muscle. I. Acetylcholine-activated channels

The properties of acetylcholine-activated excitatory currents on the gm1 muscle of three marine decapod crustaceans, the spiny lobsters Panulirus argus and interruptus, and the crab Cancer borealis, were examined using either noise analysis, analysis of synaptic current decays, or analysis of the voltage dependence of ionophoretically activated cholinergic conductance increases. The apparent mean channel open time (tau n) obtained from noise analysis at -80 mV and 12 degrees C was approximately 13 ms; tau n was prolonged e-fold for about every 100-mV hyperpolarization in membrane potential; tau n was prolonged e- fold for every 10 degrees C decrease in temperature. Gamma, the single- channel conductance, at 12 degrees C was approximately 18 pS and was not affected by voltage; gamma was increased approximately 2.5-fold for every 10 degrees C increase in temperature. Synaptic currents decayed with a single exponential time course, and at -80 mV and 12 degrees C, the time constant of decay of synaptic currents, tau ejc, was approximately 14-15 ms and was prolonged e-fold about every 140-mV hyperpolarization; tau ejc was prolonged about e-fold for every 10 degrees C decrease in temperature. The voltage dependence of the amplitude of steady-state cholinergic currents suggests that the total conductance increase produced by cholinergic agonists is increased with hyperpolarization. Compared with glutamate channels found on similar decapod muscles (see the following article), the acetylcholine channels stay open longer, conduct ions more slowly, and are more sensitive to changes in the membrane potential.     

Spontaneous activation of light-sensitive channels in Drosophila photoreceptors

In Drosophila photoreceptors light induces phosphoinositide hydrolysis and activation of Ca(2+)-permeable plasma membrane channels, one class of which is believed to be encoded by the trp gene. We have investigated the properties of the light-sensitive channels under conditions where they are activated independently of the transduction cascade. Whole-cell voltage clamp recordings were made from photoreceptors in a preparation of dissociated Drosophila ommatidia. Within a few minutes of establishing the whole-cell configuration, there is a massive spontaneous activation of cation-permeable channels. When clamped near resting potential, this "rundown current" (RDC) accelerates over several seconds, peaks, and then relaxes to a steady- state which lasts indefinitely (many minutes). The RDC is invariably associated with a reduction in sensitivity to light by at least 100- fold. The RDC has a similar absolute magnitude, reversal potential, and voltage dependence to the light-induced current, suggesting that it is mediated by the same channels. The RDC is almost completely (> or = 98%) blocked by La3+ (10-20 microM) and is absent, or reduced and altered in the trp mutant (which lacks a La(3+)-sensitive light- dependent Ca2+ channel), suggesting that it is largely mediated by the trp-dependent channels. Power spectra of the steady-state noise in the RDC can be fitted by simple Lorentzian functions consistent with random channel openings. The variance/mean ratio of the RDC noise suggests the underlying events (channels) have conductances of approximately 1.5-4.5 pS in wild-type (WT), but 12-30 pS in trp photoreceptors. Nevertheless, the power spectra of RDC noise in WT and trp are indistinguishable, in both cases being fitted by the sum of two Lorentzians with a major time constant (effective "mean channel open time") of 1-2 ms and a minor component at higher frequencies (approximately 0.2 ms). This implies that the noise in the WT RDC may actually be dominated by non-trp- dependent channels and that the trp-dependent channels may be of even lower unit conductance.     

Dispersion of latencies in photoreceptors of Limulus and the adapting- bump model

To light stimuli of very low intensity, Limulus photoreceptors give a voltage response with a fluctuating delay. This phenomenon has been called "latency dispersion." If the generator potential is the superposition of discrete voltage events ("bumps"), and if the effect of light upon bump size is negligible, then the latency dispersion and the bump shape completely characterize the frequency response to sinusoidal flicker. For very low light intensities, the latency dispersion of the bumps, the bump shape, and the frequency response are measured. It is found that for data obtained at 20 degrees C, the frequency response can be accounted for completely by the latency dispersion and by the bump shape derived from steady-state noise characteristics. At 10 degrees C, the time scale of the response of the photoreceptor is lengthened. The dispersion of latencies and the bump shape are found not to have the same temperature dependence. However, just as those measured at 20 degrees C, the bump shape and the dispersion of latencies measured at 10 degrees C can predict the frequency response measured under the same conditions. These results strongly suggest that the major mechanisms involved in the generator potential are the latency process and the bump process. At high light intensities, the time scale of the generator potential shortens. The decrease in time scale of the generator potential can be attributed to the decreases in time scales of the bumps and of the latency dispersion process.     

Newly identified steady-state potassium channels in rat hippocampal neurons.

We report two new types of potassium channels in cultured hippocampal neurons of rat. Both channels occurred in the soma membrane of these cells at very low density. They were active in steady-state conditions, within a wide voltage range that included the resting membrane potential. Their open probability was enhanced by membrane depolarization, but not influenced by Ca ions. In symmetrical 150 mM KCl the channels showed a slope conductance of ca. 40 and 80 pS, respectively. Current-voltage relations of both K channels show a negative slope at high positive voltages.     

Intrinsic gating of inward rectifier in bovine pulmonary artery endothelial cells in the presence or absence of internal Mg2+

Inward rectifier (IR) currents were studied in bovine pulmonary artery endothelial cells in the whole-cell configuration of the patch-clamp technique with extracellular K+ concentrations, [K+]o, ranging from 4.5 to 160 mM. Whether the concentration of free Mg2+ in the intracellular solution, [Mg2+]i, was 1.9 mM or nominally 0, the IR exhibited voltage- and time-dependent gating. The IR conductance was activated by hyperpolarization and deactivated by depolarization. Small steady-state outward IR currents were present up to approximately 40 mV more positive than the K+ reversal potential, EK, regardless of [Mg2+]i. Modeled as a first-order C in equilibrium O gating process, both the opening rate, alpha, and the closing rate, beta, were exponentially dependent on voltage, with beta more steeply voltage dependent, changing e-fold for 9 mV compared with 18 mV for an e-fold change in alpha. Over all [K+]o studied, the voltage dependence of alpha and beta shifted along with EK, as is characteristic of IR channels in other cells. The steady-state voltage dependence of the gating process was well described by a Boltzmann function. The half-activation potential was on average approximately 7 mV negative to the observed reversal potential in all [K+]o regardless of [Mg2+]i. The activation curve was somewhat steeper when Mg-free pipette solutions were used (slope factor, 4.3 mV) than when pipettes contained 1.9 mM Mg2+ (5.2 mV). The simplest interpretation of these data is that IR channels in bovine pulmonary artery endothelial cells have an intrinsic gating mechanism that is not due to Mg block.     

Single channel characteristics of a high conductance anion channel in "sarcoballs"

Previously undescribed high conductance single anion channels from frog skeletal muscle sarcoplasmic reticulum (SR) were studied in native membrane using the "sarcoball" technique (Stein and Palade, 1988). Excised inside-out patches recorded in symmetrical 200 mM TrisCl show the conductance of the channel''s predominant state was 505 +/- 25 pS (n = 35). From reversal potentials, the Pcl/PK ratio was 45. The slope conductance vs. Cl- ion concentration curve saturates at 617 pS, with K0.5 estimated at 77 mM. The steady-state open probability (Po) vs. holding potential relationship produces a bell-shaped curve, with Po values reaching a maximum near 1.0 at 0 mV, and falling off to 0.05 at +/- 25 mV. Kinetic analysis of the voltage dependence reveals that while open time constants are decreased somewhat by increases in potential, the largest effect is an increase in long closed times. Despite the channel''s high conductance, it maintains a moderate selectivity for smaller anions, but will not pass larger anions such as gluconate, as determined by reversal-potential shifts. At least two substates different from the main open level are distinguishable. These properties are unlike those described for mitochondrial voltage- dependent anion channels or skeletal muscle surface membrane Cl channels and since SR Ca channels are present in equally high density in sarcoball patches, we propose these sarcoball anion channels originate from the SR. Preliminary experiments recording currents from frog SR anion channels fused into liposomes indicate that either biochemical isolation and/or alterations in lipid environment greatly decrease the channel''s voltage sensitivity. These results help underline the potential significance of using sarcoballs to study SR channels. The steep voltage sensitivity of the sarcoball anion channel suggests that it could be more actively involved in the regulation of Ca2+ transport by the SR.     

Limitations of the dual voltage clamp method in assaying conductance and kinetics of gap junction channels.

The electrical properties of gap junctions in cell pairs are usually studied by means of the dual voltage clamp method. The voltage across the junctional channels, however, cannot be controlled adequately due to an artificial resistance and a natural resistance, both connected in series with the gap junction. The access resistances to the cell interior of the recording pipettes make up the artificial resistance. The natural resistance consists of the cytoplasmic access resistances to the tightly packed gap junction channels in both cells. A mathematical model was constructed to calculate the actual voltage across each gap junction channel. The stochastic open-close kinetics of the individual channels were incorporated into this model. It is concluded that even in the ideal case of complete compensation of pipette series resistance, the number of channels comprised in the gap junction may be largely underestimated. Furthermore, normalized steady-state junctional conductance may be largely overestimated, so that transjunctional voltage dependence is easily masked. The model is used to discuss conclusions drawn from dual voltage clamp experiments and offers alternative explanations for various experimental observations.     

Interaction of scorpion alpha-toxins with cardiac sodium channels: binding properties and enhancement of slow inactivation

The effects of the scorpion alpha-toxins Lqh II, Lqh III, and LqhalphaIT on human cardiac sodium channels (hH1), which were expressed in human embryonic kidney (HEK) 293 cells, were investigated. The toxins removed fast inactivation with EC(50) values of <2.5 nM (Lqh III), 12 nM (Lqh II), and 33 nM (LqhalphaIT). Association and dissociation rates of Lqh III were much slower than those of Lqh II and LqhalphaIT, such that Lqh III would not dissociate from the channel during a cardiac activation potential. The voltage dependence of toxin dissociation from hH1 channels was nearly the same for all toxins tested, but it was different from that found for skeletal muscle sodium channels (muI; Chen et al. 2000). These results indicate that the voltage dependence of toxin binding is a property of the channel protein. Toxin dissociation remained voltage dependent even at high voltages where activation and fast inactivation is saturated, indicating that the voltage dependence originates from other sources. Slow inactivation of hH1 and muI channels was significantly enhanced by Lqh II and Lqh III. The half-maximal voltage of steady-state slow inactivation was shifted to negative values, the voltage dependence was increased, and, in particular for hH1, slow inactivation at high voltages became more complete. This effect exceeded an expected augmentation of slow inactivation owing to the loss of fast inactivation and, therefore, shows that slow sodium channel inactivation may be directly modulated by scorpion alpha-toxins.     

Voltage noise influences action potential duration in cardiac myocytes

Stochastic gating of ion channels introduces noise to membrane currents in cardiac muscle cells (myocytes). Since membrane currents drive membrane potential, noise thereby influences action potential duration (APD) in myocytes. To assess the influence of noise on APD, membrane potential is in this study formulated as a stochastic process known as a diffusion process, which describes both the current-voltage relationship and voltage noise. In this framework, the response of APD voltage noise and the dependence of response on the shape of the current-voltage relationship can be characterized analytically. We find that in response to an increase in noise level, action potential in a canine ventricular myocytes is typically prolonged and that distribution of APDs becomes more skewed towards long APDs, which may lead to an increased frequency of early after-depolarization formation. This is a novel mechanism by which voltage noise may influence APD. The results are in good agreement with those obtained from more biophysically-detailed mathematical models, and increased voltage noise (due to gating noise) may partially underlie an increased incidence of early after-depolarizations in heart failure.     

Voltage-sensitive potassium channels in Limulus ventral photoreceptors

The steady-state slope conductance of Limulus ventral photoreceptors increases markedly when the membrane is depolarized from rest. The ionic basis of this rectification has been examined with a voltage-clamp technique. Tail currents that occur when membrane potential is repolarized after having been depolarized have been identified. The tail currents reverse direction at a voltage that becomes more positive when Ko is increased. Rectification is reduced by extracellular 4-aminopyridine and by intracellular injection of tetra-ethyl-ammonium (TEA). These results indicate that the membrane rectification around resting potential is due primarily to voltage-sensitive K+ channels. The increase in gK caused by depolarization is not mediated by a voltage-dependent rise in in Cai++, since intracellular injection of Ca++ causes a decrease rather than an increase in slope conductance. TEA can be used to examine the functional role of the K+ channels because it blocks them without substantially affecting the light-activated Na+ conductance. The effect of TEA on response-intensity curves shows that the K+ channels serve to compress the voltage range of receptor potentials.     

Can quantum-bumps in photoreceptors be reconstructed from noise-data?

The method of reconstructing quantum bumps in photoreceptor cells from noise data by making use of shot noise theory is critically reviewed. The application of this method produces results irrespective of whether the conditions for reconstructing bumps by the method are satisfied or not and even irrespective of whether at high stimulus intensities quantum bumps exist or not. We argue that at high intensities the concept of quantum bumps indeed becomes physically meaningless and degenerates to a purely mathematical concept. In order to investigate the meaning of the results of the reconstruction method, we submit it to a test model for which bumps and single channel opening events can be evaluated analytically. By comparing the analytical results of the test model with that of the reconstruction method applied to the test model we find: (1) even at low intensities, the reconstructed bump values deviate from the analytical results by up to an order of magnitude due to the variability of the bumps, (2) at high intensities, the reconstruction method produces single chennel opening events rather than anything like a quantum bump. We also find, however, that there is no continuous transition from a bump at low intensities to a single channel event at high intensities.     

Maxi K+ channels and their relationship to the apical membrane conductance in Necturus gallbladder epithelium

Using the patch-clamp technique, we have identified large-conductance (maxi) K+ channels in the apical membrane of Necturus gallbladder epithelium, and in dissociated gallbladder epithelial cells. These channels are more than tenfold selective for K+ over Na+, and exhibit unitary conductance of approximately 200 pS in symmetric 100 mM KCl. They are activated by elevation of internal Ca2+ levels and membrane depolarization. The properties of these channels could account for the previously observed voltage and Ca2+ sensitivities of the macroscopic apical membrane conductance (Ga). Ga was determined as a function of apical membrane voltage, using intracellular microelectrode techniques. Its value was 180 microS/cm2 at the control membrane voltage of -68 mV, and increased steeply with membrane depolarization, reaching 650 microS/cm2 at -25 mV. We have related maxi K+ channel properties and Ga quantitatively, relying on the premise that at any apical membrane voltage Ga comprises a leakage conductance and a conductance due to maxi K+ channels. Comparison between Ga and maxi K+ channels reveals that the latter are present at a surface density of 0.09/microns 2, are open approximately 15% of the time under control conditions, and account for 17% of control Ga. Depolarizing the apical membrane voltage leads to a steep increase in channel steady-state open probability. When correlated with patch-clamp studies examining the Ca2+ and voltage dependencies of single maxi K+ channels, results from intracellular microelectrode experiments indicate that maxi K+ channel activity in situ is higher than predicted from the measured apical membrane voltage and estimated bulk cytosolic Ca2+ activity. Mechanisms that could account for this finding are proposed.     

A new look at the mechanism of activation and inactivation of voltage-gated ion channels.

Studies on the kinetics of activation and inactivation of the sodium channels of the squid giant axon, on the sodium gating current, and on the properties of the non-inactivating steady-state current, are briefly reviewed. Taken in conjunction with recent evidence on the structure of voltage-gated ion channels, they have led to the development of a series-parallel model of the sodium channel that can be regarded as a modernized version of the Hodgkin-Huxley model, with some novel features. It is suggested that activation results from conformational changes brought about by the four S4 voltage sensors operating in parallel, each of which makes two discrete steps to reach the fully activated state of the channel. There follows a voltage-independent hydration step, and the channel is ready to open. Inactivation is a potential-dependent process involving a third transition of voltage sensor S4d alone, which, rather than bringing a ball and chain blocking group into position to close the channels, serves to switch the system so that it passes from an initial activated mode, in which there is a high probability of arriving at an open state with a brief latency, to a second steady-state mode, in which the probability of opening is very much lower.     

On the Na+,K+ pump in fluctuating membrane potentials

The present work investigates the usefulness of noise in the activity of the Na+,K+ pump. Random gating activity of the neighboring ion channels causes local fluctuations of the electric potential. They are modeled by a Markovian symmetric dichotomic noise, added to the membrane potential. The noise-averaged pump current is calculated for a general rectangular voltage signal and the model parameters of the effective two-state enzyme cycle are tuned to fit experimental results. Then, using these parameters, the amount of transported charge is calculated, and studied as a function of noise intensity. Signal and noise characteristics are identified at which fluctuations enhance pump activity. The biological impact of this phenomenon seems to be absent in physiological conditions for it occurs at noise amplitudes over 50 mV, which are unlikely to appear due to ion channels. However, under some conditions, externally applied dichotomic noise of intensity about 150 mV may sensibly increase the quantity of transported charge.     

Kinetic isoforms of intramembrane charge in intact amphibian striated muscle

The effects of the ryanodine receptor (RyR) antagonists ryanodine and daunorubicin on the kinetic and steady-state properties of intramembrane charge were investigated in intact voltage-clamped frog skeletal muscle fibers under conditions that minimized time-dependent ionic currents. A hypothesis that RyR gating is allosterically coupled to configurational changes in dihydropyridine receptors (DHPRs) would predict that such interactions are reciprocal and that RyR modification should influence intramembrane charge. Both agents indeed modified the time course of charging transients at 100-200-microM concentrations. They independently abolished the delayed charging phases shown by q gamma currents, even in fibers held at fully polarized, -90-mV holding potentials; such waveforms are especially prominent in extracellular solutions containing gluconate. Charge movements consistently became exponential decays to stable baselines in the absence of intervening inward or other time-dependent currents. The steady-state charge transfers nevertheless remained equal through the ON and the OFF parts of test voltage steps. The charge-voltage function, Q(VT), shifted by approximately +10 mV, particularly through those test potentials at which delayed q gamma currents normally took place but retained steepness factors (k approximately 8.0 to 10.6 mV) that indicated persistent, steeply voltage-dependent q gamma contributions. Furthermore, both RyR antagonists preserved the total charge, and its variation with holding potential, Qmax (VH), which also retained similarly high voltage sensitivities (k approximately 7.0 to 9.0 mV). RyR antagonists also preserved the separate identities of q gamma and q beta species, whether defined by their steady-state voltage dependence or inactivation or pharmacological properties. Thus, tetracaine (2 mM) reduced the available steady-state charge movement and gave shallow Q(VT) (k approximately 14 to 16 mV) and Qmax (VH) (k approximately 14 to 17 mV) curves characteristic of q beta charge. These features persisted with exposure to test agent. Finally, q gamma charge movements showed steep voltage dependences with both activation (k approximately 4.0 to 6.5 mV) and inactivation characteristics (k approximately 4.3 to 6.6 mV) distinct from those shown by the remaining q beta charge, whether isolated through differential tetracaine sensitivities, or the full approximation of charge-voltage data to the sum of two Boltzmann distributions. RyR modification thus specifically alters q gamma kinetics while preserving the separate identities of steady-state q beta and q gamma charge. These findings permit a mechanism by which transverse tubular voltage provides the primary driving force for configurational changes in DHPRs, which might produce q gamma charge movement. However, they attribute its kinetic complexities to the reciprocal allosteric coupling by which DHPR voltage sensors and RyR-Ca2+ release channels might interact even though these receptors reside in electrically distinct membranes. RyR modification then would still permit tubular voltage change to drive net q gamma charge transfer but would transform its complex waveforms into simple exponential decays.     

Frequency bandwidth limitation of external pulse electric fields in cylindrical micro-channel electrophoresis with analyte velocity modulation

In capillary electrophoresis, effective optical signal quality improvement is obtained when high frequency (>100 Hz) external pulse fields modulate analyte velocities with synchronous lock-in detection. However, the pulse frequency is constrained under a critical value corresponding to the time required for the bulk viscous flow, which arises due to viscous momentum diffusion from the electro-osmotic slip in the Debye layer, to reach steady-state. By solving the momentum diffusion equation for transient bulk flow in the micro-channel, we show that this set-in time to steady-state and hence, the upper limit for the pulse frequency is dependent on the characteristic diffusion length scale and therefore the channel geometry; for cylindrical capillaries, the set-in time is approximately one half of that for rectangular slot channels. From our estimation of the set-in time and hence the upper frequency modulation limit, we propose that the half width of planar channels does not exceed 100 microm and that the radii of cylindrical channels be limited to 140 microm such that there is a finite working bandwidth range above 100 Hz and below the upper limit in order for flicker noise to be effectively suppressed.