Cable theory in neurons with active,linearized membranes

This investigation aims at exploring some of the functional consequences of single neurons containing active, voltage dependent channels for information processing. Assuming that the voltage change in the dendritic tree of these neurons does not exceed a few millivolts, it is possible to linearize the non-linear channel conductance. The membrane can then be described in terms of resistances, capacitances and inductances, as for instance in the small-signal analysis of the squid giant axon. Depending on the channel kinetics and the associated ionic battery the linearization yields two basic types of membrane: a membrane modeled by a collection of resistances and capacitances and membranes containing in addition to these components inductances. Under certain specified conditions the latter type of membrane gives rise to a membrane impedance that displays a prominent maximum at some nonzero resonant frequency f _max. We call this type of membrane quasi-active, setting it apart from the usual passive membrane. We study the linearized behaviour of active channels giving rise to quasi-active membranes in extended neuronal structures and consider several instances where such membranes may subserve neuronal function: 1. The resonant frequency of a quasi-active membrane increases with increasing density of active channels. This might be one of the biophysical mechanisms generating the large range over which hair cells in the vertebrate cochlea display frequency tuning. 2. The voltage recorded from a cable with a quasi-active membrane can be proportional to the temporal derivative of the injected current. 3. We modeled a highly branched dendritic tree (-ganglion cell of the cat retina) using a quasi-active membrane. The voltage attenuation from a given synaptic site to the soma decreases with increasing frequency up to the resonant frequency, in sharp contrast to the behaviour of passive membranes. This might be the underlying biophysical mechanism of receptive fields whose dimensions are large for rapid signals but contract to a smaller area for slow signals as suggested by Detwiler et al. (1978).     

Spike latency and jitter of neuronal membrane patches with stochastic Hodgkin-Huxley channels

Ion channel stochasticity can influence the voltage dynamics of neuronal membrane, with stronger effects for smaller patches of membrane because of the correspondingly smaller number of channels. We examine this question with respect to first spike statistics in response to a periodic input of membrane patches including stochastic Hodgkin-Huxley channels, comparing these responses to spontaneous firing. Without noise, firing threshold of the model depends on frequency—a sinusoidal stimulus is subthreshold for low and high frequencies and suprathreshold for intermediate frequencies. When channel noise is added, a stimulus in the lower range of subthreshold frequencies can influence spike output, while high subthreshold frequencies remain subthreshold. Both input frequency and channel noise strength influence spike timing. Specifically, spike latency and jitter have distinct minima as a function of input frequency, showing a resonance like behavior. With either no input, or low frequency subthreshold input, or input in the low or high suprathreshold frequency range, channel noise reduces latency and jitter, with the strongest impact for the lowest input frequencies. In contrast, for an intermediate range of suprathreshold frequencies, where an optimal input gives a minimum latency, the noise effect reverses, and spike latency and jitter increase with channel noise. Thus, a resonant minimum of the spike response as a function of frequency becomes more pronounced with less noise. Spike latency and jitter also depend on the initial phase of the input, resulting in minimal latencies at an optimal phase, and depend on the membrane time constant, with a longer time constant broadening frequency tuning for minimal latency and jitter. Taken together, these results suggest how stochasticity of ion channels may influence spike timing and thus coding for neurons with functionally localized concentrations of channels, such as in “hot spots” of dendrites, spines or axons.     

Computer simulations of neuron-glia interactions mediated by ion flux

Extracellular potassium concentration, [K⁺]_o, and intracellular calcium, [Ca²⁺]_i, rise during neuron excitation, seizures and spreading depression. Astrocytes probably restrain the rise of K⁺ in a way that is only partly understood. To examine the effect of glial K⁺ uptake, we used a model neuron equipped with Na⁺, K⁺, Ca²⁺ and Cl⁻ conductances, ion pumps and ion exchangers, surrounded by interstitial space and glia. The glial membrane was either “passive”, incorporating only leak channels and an ion exchange pump, or it had rectifying K⁺ channels. We computed ion fluxes, concentration changes and osmotic volume changes. Increase of [K⁺]_o stimulated the glial uptake by the glial 3Na/2K ion pump. The [K⁺]_o flux through glial leak and rectifier channels was outward as long as the driving potential was outwardly directed, but it turned inward when rising [K⁺]_o/[K⁺]_i ratio reversed the driving potential. Adjustments of glial membrane parameters influenced the neuronal firing patterns, the length of paroxysmal afterdischarge and the ignition point of spreading depression. We conclude that voltage gated K⁺ currents can boost the effectiveness of the glial “potassium buffer” and that this buffer function is important even at moderate or low levels of excitation, but especially so in pathological states.     

Zinc ions block H⁺/OH⁻ channels in Chara australis

Chara australis cells exposed to media of pH 10 and above exhibit high conductance, arising from the opening of H⁺/OH^‐ channels in the plasma membrane. This high conductance can be totally inhibited by 1.0 mm ZnCl₂ and restored by 0.5 mm 2‐mercaptoethanol (ME). Important for carbon fixation, H⁺/OH^‐ channels play a key role in cell pH banding. Banding was also shown to be abolished by 1.0 mm ZnCl₂ and restored in some cells by ME. The proton pump is also involved in banding, but was little affected by ZnCl₂ over the periods needed for the inhibition of H⁺/OH^‐ channels. Previously, we postulated that H⁺/OH^‐ channels open transiently at the onset of saline stress in salt‐sensitive C. australis, causing membrane potential difference (PD) noise; and remain open in latter stages of saline stress, contributing to cell deterioration. ZnCl₂ totally inhibited the saline noise and the upwardly concave I/V characteristics associated with the putative H⁺/OH^‐ currents. Again, ME reversed both these effects. We discuss the mode of action of zinc ions and ME with reference to animal voltage‐gated H⁺ channels and water channels.     

Three Types of Single Voltage-Dependent Potassium Channels in the Sarcolemma of Frog Skeletal Muscle

Patch-clamp experiments in the sarcolemma of frog skeletal muscle evidenced the presence of three types of voltage-dependent single-channel K⁺ currents. According to their unitary conductance at a membrane voltage of +40 mV, we classified them as 16-, 13-, and 7-pS K⁺ channels. The 16-pS K⁺ channels are active close to a membrane voltage of −80 mV and they do not become inactivated during voltage pulses of 100 ms. Within 10 min after beginning the recording, these channels developed rundown with an exponential time course. The 13-pS K⁺ channels are active near −60 mV; upon a 100-ms depolarization, they exhibited inactivation with an approximate exponential time course. The 7-pS K⁺ channels were recorded at voltages positive to 0 mV. In patches containing all three types of K⁺ channels, the ensemble average currents resemble the kinetic properties of the macroscopic delayed rectifier K⁺ currents recorded in skeletal muscle and other tissues. In conclusion, the biophysical properties of unitary K⁺ currents suggest that these single-channel K⁺ currents may underlie the macroscopic delayed K⁺ currents in frog skeletal muscle fibers. In addition, since the 16- and 13-pS channels were more frequently recorded, both are the main contributors to the delayed K⁺ currents.     

Ion behavior in the selectivity filter of HCN1 channels

Hyperpolarization-activated cyclic-nucleotide gated channels (HCNs) are responsible for the generation of pacemaker currents (I_f or I_h) in cardiac and neuronal cells. Despite the overall structural similarity to voltage-gated potassium (Kv) channels, HCNs show much lower selectivity for K⁺ over Na⁺ ions. This increased permeability to Na⁺ is critical to their role in membrane depolarization. HCNs can also select between Na⁺ and Li⁺ ions. Here, we investigate the unique ion selectivity properties of HCNs using molecular-dynamics simulations. Our simulations suggest that the HCN1 pore is flexible and dilated compared with Kv channels with only one stable ion binding site within the selectivity filter. We also observe that ion coordination and hydration differ within the HCN1 selectivity filter compared with those in Kv and cyclic-nucleotide gated channels. Additionally, the C358T mutation further stabilizes the symmetry of the binding site and provides a more fit space for ion coordination, particularly for Li⁺.     

Theory of transport noise in membrane channels with open-closed kinetics

A theoretical approach to transport noise in kinetic systems, which has recently been developed, is applied to electric fluctuations around steady-states in membrane channels with different conductance states. The channel kinetics may be simple two state (open-closed) kinetics or more complicated. The membrane channel is considered as a sequence of binding sites separated by energy barriers over which the ions have to jump according to the usual single-file diffusion model. For simplicity the channels are assumed to act independently. In the special case of ionic movement fast compared with the channel open-closed kinetics the results agree with those derived from the usual Master equation approach to electric fluctuations in nerve membrane channels.For the simple model of channels with one binding site and two energy barries the coupling between the fluctuations coming from the open-closed kinetics and from the jump diffusion is investigated.     

Interaction of local anesthetics with the K+ channel pore domain

Local anesthetics and related drugs block ionic currents of Na⁺, K⁺ and Ca²⁺ conducted across the cell membrane by voltage-dependent ion channels. Many of these drugs bind in the permeation pathway, occlude the pore and stop ion movement. However channel-blocking drugs have also been associated with decreased membrane stability of certain tetrameric K⁺ channels, similar to the destabilization of channel function observed at low extracellular K⁺ concentration. Such drug-dependent stability may result from electrostatic repulsion of K⁺ from the selectivity filter by a cationic drug molecule bound in the central cavity of the channel. In this study we used the pore domain of the KcsA K⁺ channel protein to test this hypothesis experimentally with a biochemical assay of tetramer stability and theoretically by computational simulation of local anesthetic docking to the central cavity. We find that two common local anesthetics, lidocaine and tetracaine, promote thermal dissociation of the KcsA tetramer in a K⁺-dependent fashion. Docking simulations of these drugs with open, open-inactivated and closed crystal structures of KcsA yield many energetically favorable drug-channel complexes characterized by nonbonded attraction to pore-lining residues and electrostatic repulsion of K⁺. The results suggest that binding of cationic drugs to the inner cavity can reduce tetramer stability of K⁺ channels.     

Non-linear Membrane Properties in Entorhinal Cortical Stellate Cells Reduce Modulation of Input-Output Responses by Voltage Fluctuations

The presence of voltage fluctuations arising from synaptic activity is a critical component in models of gain control, neuronal output gating, and spike rate coding. The degree to which individual neuronal input-output functions are modulated by voltage fluctuations, however, is not well established across different cortical areas. Additionally, the extent and mechanisms of input-output modulation through fluctuations have been explored largely in simplified models of spike generation, and with limited consideration for the role of non-linear and voltage-dependent membrane properties. To address these issues, we studied fluctuation-based modulation of input-output responses in medial entorhinal cortical (MEC) stellate cells of rats, which express strong sub-threshold non-linear membrane properties. Using in vitro recordings, dynamic clamp and modeling, we show that the modulation of input-output responses by random voltage fluctuations in stellate cells is significantly limited. In stellate cells, a voltage-dependent increase in membrane resistance at sub-threshold voltages mediated by Na⁺ conductance activation limits the ability of fluctuations to elicit spikes. Similarly, in exponential leaky integrate-and-fire models using a shallow voltage-dependence for the exponential term that matches stellate cell membrane properties, a low degree of fluctuation-based modulation of input-output responses can be attained. These results demonstrate that fluctuation-based modulation of input-output responses is not a universal feature of neurons and can be significantly limited by subthreshold voltage-gated conductances.     

Exploring voltage-dependent ion channels in silico by hysteretic conductance

Kinetic models of voltage-dependent ion channels are normally inferred from time records of macroscopic current relaxation or microscopic single channel data. A complementary explorative approach is outlined. Hysteretic conductance refers to conductance delays in response to voltage changes, delays at either macroscopic or microscopic levels of observation. It enables complementary assessments of model assumptions and gating schemes of voltage-dependent channels, e.g. independent versus cooperative gating, and multiple gating modes. Under the Hodgkin-Huxley condition of independent gating, and under ideal measurement conditions, hysteretic conductance makes it also possible to estimate voltage-dependent rate functions. The argument is mainly theoretical, based on experimental observations, and illustrated by simulations of Markov kinetic models.     

Low-frequency voltage noise in a mammalian bone cell clone

Measurements were made of plasma membrane voltage noise in cells of a bone cell clone. The measurements were made under conditions intended to approximate in vivo conditions more closely than in previous electrical measurements on small mammalian cells. Mononuclucell of normal size, imbedded in a collagen matrix, were used. The electrical state of the cell membrane under normal conditions was characterized by low-frequency random fluctuations (noise) of high magnitude. Hyperpolarizing spikes were observed in some cells. Power spectrum analysis revealed that the random fluctuations were actually a sum of incoherent spike patterns, with spikes of the same time width as those seen in the clearly spiking patterns. This analysis, combined with similar measurements in a high [K⁺], low [Na⁺] medium, showed that the fluctuation/spiking phenomenon resulted from modulation of K⁺ and Na⁺ transport by a control process at a level higher that that of the individual channels. This process persisted when the membrane potential was depolarized. These results indicate that the membrane potential is not part of the feedback loop producing the fluctuation/spiking phenomenon.     

Modulation of the Voltage-Dependent Anion Channel (VDAC) by Glutamate1

The voltage-dependent anion channel (VDAC), also known as mitochondrial porin, is a large channel permeable to anions, cations, ATP, and other metabolites. VDAC was purified from sheep brain synaptosomes or rat liver mitochondria using a reactive red-agarose column, in addition to the hydroxyapatitate column. The red-agarose column allowed further purification (over 98%), concentration of the protein over ten-fold, decreasing Triton X-100 concentration, and/or replacing Triton X-100 with other detergents, such as Nonidet P-40 or octylglucoside. This purified VDAC reconstituted into planar-lipid bilayer, had a unitary maximal conductance of 3.7 ± 0.1 nS in 1 M NaCl, at 10 mV and was permeable to both large cations and anions. In the maximal conducting state, the permeability ratios for Na⁺, acetylcholine⁺, dopamine,⁺ and glutamate^–, relative to Cl^–, were estimated to be 0.73, 0.6, 0.44, and 0.4, respectively. In contrast, in the subconducting state, glutamate^– was impermeable, while the relative permeability to acetylcholine⁺ increased and to dopamine⁺ remained unchanged. At the high concentrations (0.1–0.5 M) used in the permeability experiments, glutamate eliminated the bell shape of the voltage dependence of VDAC channel conductance. Glutamate at concentrations of 1 to 20 mM, in the presence of 1 M NaCl, was found to modulate the VDAC channel activity. In single-channel experiments, at low voltages (±10 mV), glutamate induced rapid fluctuations of the channel between the fully open state and long-lived low-conducting states or short-lived closed state. Glutamate modification of the channel activity, at low voltages, is dependent on voltage, requiring short-time (20–60 sec) exposure of the channel to high membrane potentials. The effect of glutamate is specific, since it was observed in the presence of 1 M NaCl and it was not obtained with aspartate or GABA. These results suggest that VDAC possesses a specific glutamate-binding site that modulates its activity.     

Gating in iodate-modified single cardiac Na+ channels

Summary Elementary Na⁺ currents were recorded at 19°C during 220-msec lasting step depolarizations in cell-attached and inside-out patches from cultured neonatal rat cardiocytes in order to study the modifying influence of iodate, bromate and glutaraldehyde on single cardiac Na⁺ channels.Iodate (10 mmol/liter) removed Na⁺ inactivation and caused repetitive, burst-like channel activity after treating the cytoplasmic channel surface. In contrast to normal Na⁺ channels under control conditions, iodate-modified Na⁺ channels attain two conducting states, a short-lasting one with a voltage-independent lifetime close to 1 msec and, likewise tested between –50 and +10 mV, a long-lasting one being apparently exponentially dependent on voltage. Channel modification by bromate (10 mmol/liter) and glutaraldehyde (0.5 mmol/liter) also included the occurrence of two open states. Also, burst duration depended apparently exponentially on voltage and increased when shifting the membrane in the positive direction, but there was no evidence for two bursting states. Chemically modified Na⁺ channels retain an apparently normal unitary conductance (12.8±0.5 pS). Of the two substates observed, one of them is remarkable in that it is mostly attained from full-state openings and is very short living in nature; the voltage-independent lifetime was close to 2 msec. Despite removal of inactivation, open probability progressively declined during membrane depolarization. The underlying deactivation process is strongly voltage sensitive but, in contrast to slow Na⁺ inactivation, responds to a voltage shift in the positive direction with a retardation in kinetics. Chemically modified Na⁺ channels exhibit a characteristic bursting state much shorter than in DPI-modified Na⁺ channels, a difference not consistent with the hypothesis of common kinetic properties in noninactivating Na⁺ channels.     

Regulation of K+ channels in the basolateral membrane ofNecturus oxyntic cells

Summary Patch-clamp methods were used to study single-channel events in isolated oxyntic cells and gastric glands fromNecturus maculosa. Cell-attached, excised inside-out and outside-out patches from the basolateral membrane frequently contained channels which had conductances of 67±21 pS in 24% of the patches and channels of smaller conductance, 33±6 pS in 56% of the patches. Channels in both classes were highly selective for K⁺ over Na⁺ and Cl^–, and shared linear current-voltage relations. The 67-pS channel was activated by membrane depolarization, whereas the activity of the 33-pS channel was relatively voltage independent. The larger conductance channels were activated by intracellular Ca²⁺ in the range between 5 and 500nm, but unaffected by cAMP. The smaller conductance channels were activated by cAMP, but not Ca²⁺. The presence of K⁺ channels in the basolateral membrane which are regulated by these known second messengers can account for the increase in conductance and the hyperpolarization of the membrane observed upon secretagogue stimulation.     

Non-equilibrium voltage noise generated by ion transport through pores

In this paper, we describe a systematic approach to the theoretical analysis of non-equilibrium voltage noise that arises from ions moving through pores in membranes. We assume that an ion must cross one or two barriers in the pore in order to move from one side of the membrane to the other. In our analysis, we consider the following factors: a) surface charge as a variable in the kinetic equations, b) linearization of the kinetic equations, c) master equation approach to fluctuations. To analyze the voltage noise arising from ion movement through a two barrier (i.e., one binding site) pore, we included the effects of ions in the channel's interior on the voltage noise. The current clamp is considered as a white noise generating additional noise in the system. In contrast to what is found for current noise, at low frequencies the voltage noise intensity is reduced by increasing voltage across the membrane. With this approach, we demonstrate explicity for the examples treated that, apart from additional noise generated by the current clamp, the non-equilibrium voltage fluctuations can be related to the current fluctuations by the complex admittance.     

Glucose Deprivation Activates Diversity of Potassium Channels in Cultured Rat Hippocampal Neurons

1. Glucose is one of the most important substrates for generating metabolic energy required for the maintenance of cellular functions. Glucose-mediated changes in neuronal firing pattern have been observed in the central nervous system of mammals. K⁺ channels directly regulated by intracellular ATP have been postulated as a linkage between cellular energetic metabolism and excitability; the functional roles ascribed to these channels include glucose-sensing to regulate energy homeostasis and neuroprotection under energy depletion conditions. The hippocampus is highly sensitive to metabolic insults and is the brain region most sensitive to ischemic damage. Because the identity of metabolically regulated potassium channels present in hippocampal neurons is obscure, we decided to study the biophysical properties of glucose-sensitive potassium channels in hippocampal neurons.2. The dependence of membrane potential and the sensitivity of potassium channels to glucose and ATP in rat hippocampal neurons were studied in cell-attached and excised inside-out membrane patches.3. We found that under hypoglycemic conditions, at least three types of potassium channels were activated; their unitary conductance values were 37, 147, and 241 pS in symmetrical K⁺, and they were sensitive to ATP. For K⁺ channels with unitary conductance of 37 and 241, when the membrane potential was depolarized the longer closed time constant diminished and this produced an increase in the open-state probability; nevertheless, the 147-pS channels were not voltage-dependent.4. We propose that neuronal glucose-sensitive K⁺ channels in rat hippocampus include subtypes of ATP-sensitive channels with a potential role in neuroprotection during short-term or prolonged metabolic stress.     

Noise analysis reveals K+ channel conductance fluctuations in the apical membrane of rabbit colon

Summary In this paper we describe current fluctuations in the mammalian epithelium, rabbit descending colon. Pieces of isolated colon epithelium bathed in Na⁺ or K⁺ Ringer's solutions were studied under short-circuit conditions with the current noise spectra recorded over the range of 1–200 Hz. When the epithelium was bathed on both sides with Na⁺ Ringer's solution (the mucosal solution contained 50 m amiloride), no Lorentzian components were found in the power spectrum. After imposition of a potassium gradient across the epithelium by replacement of the mucosal solution by K⁺ Ringer's (containing 50 m amiloride), a Lorentzian component appeared with an average corner frequency,f _c=15.6±0.91 Hz and a mean plateau valueS _o=(7.04±2.94)×10^–20 A² sec/cm². The Lorentzian component was enhanced by voltage clamping the colon in a direction favorable for K⁺ entry across the apical membrane. Elimination of the K⁺ gradient by bathing the colon on both sides with K⁺ Ringer's solutions abolished the noise signal. The Lorentzian component was also depressed by mucosal addition of Cs⁺ or tetraethylammonium (TEA) and by serosal addition of Ba²⁺. The one-sided action of these K⁺ channel blockers suggests a cellular location for the fluctuating channels. Addition of nystatin to the mucosal solution abolished the Lorentzian component. Serosal nystatin did not affect the Lorentzian noise. This finding indicates an apical membrane location for the fluctuating channels. The data were similar in some respects to K⁺ channel fluctuations recorded from the apical membranes of amphibian epithelia such as the frog skin and toad gallbladder. The results are relevant to recent reports concerning transcellular potassium secretion in the colon and indicate that the colon possesses spontaneously fluctuating potassium channels in its apical membranes in parallel to the Na⁺ transport pathway.     

Ion channels as pharmacologic receptors: The chirality of drug interactions

Ion channels are pharmocologic receptors and as such exhibit stereoselective interactions with drugs. Ion channels are conformationally mobile transmembrane proteins existing in a number of open and closed states. Drug interactions with these different states may differ quantitatively and qualitatively. Stereoselectivity may not be a constant factor and may change according to channel state as determined by stimulus mode or experimental conditions. Selected examples are cited for Na⁺ and Ca²⁺ channels. © 1996 Wiley-Liss, Inc.     

Ion channels activated by osmotic and mechanical stress in membranes of opossum kidney cells

Summary For patch-clamp measurements cultured kidney (OK) cells were exposed to osmotic and mechanical stress. Superfusion of a cell in whole cell configuration with hypotonic media (190 mOsm) evokes strong depolarization, which is reversible by returning to the isotonic bath medium. In the cell-attached configuration the exposure to hypotonic media evokes up to six ion channels of homogeneous single-channel properties in the membrane patch. Subsequently, the channels became activated after a time lag of a few seconds. At an applied membrane potential of 0 mV, the corresponding membrane current is directed inward and shows a transient behavior in the time range of minutes. In the same membrane patch these ion channels can be activated by application of negative hydrostatic pressure. The channel has a single-channel conductance of about 22 pS and is permeable to Na⁺ and K⁺ as well as to Cl^–. It is suggested that volume regulation involves mechanoreceptor-operated ion channels.