Model of oscillatory activity in thalamic neurons: Role of voltage- and calcium-dependent ionic conductances

This paper describes a computer modeling study of the generation of 10 Hz oscillations in the electrical activity of guinea pig thalamic neurons in vitro. The computer model was based on experimental evidence suggesting that single thalamic neurons in guinea pig have a set of voltage- and calcium-dependent ionic conductances that is capable of generating self-sustained rhythmic oscillations. Simulation results are consistent with this hypothesis, and indicate that a model that contains dendritic calcium and calcium-dependent potassium conductances, as well as a voltage-dependent, slow sodium conductance, can indeed generate self-sustained oscillations like those seen in thalamic neurons. Moreover, simulations indicate that the occurrence of such oscillatory activity is strongly dependent on the location of the slow sodium conductance. Results predict that this slow sodium conductance is located in the dendrites.The authors express their appreciation to R. J. MacGregor for providing equations and computer programs for simulating a two-point neuronal model with active calcium-related conductances     

Co-variation of ionic conductances supports phase maintenance in stomatogastric neurons

Neuronal networks produce reliable functional output throughout the lifespan of an animal despite ceaseless molecular turnover and a constantly changing environment. Central pattern generators, such as those of the crustacean stomatogastric ganglion (STG), are able to robustly maintain their functionality over a wide range of burst periods. Previous experimental work involving extracellular recordings of the pyloric pattern of the STG has demonstrated that as the burst period varies, the inter-neuronal delays are altered proportionally, resulting in burst phases that are roughly invariant. The question whether spike delays within bursts are also proportional to pyloric period has not been explored in detail. The mechanism by which the pyloric neurons accomplish phase maintenance is currently not obvious. Previous studies suggest that the co-regulation of certain ion channel properties may play a role in governing neuronal activity. Here, we observed in long-term recordings of the pyloric rhythm that spike delays can vary proportionally with burst period, so that spike phase is maintained. We then used a conductance-based model neuron to determine whether co-varying ionic membrane conductances results in neural output that emulates the experimentally observed phenomenon of spike phase maintenance. Next, we utilized a model neuron database to determine whether conductance correlations exist in model neuron populations with highly maintained spike phases. We found that co-varying certain conductances, including the sodium and transient calcium conductance pair, causes the model neuron to maintain a specific spike phase pattern. Results indicate a possible relationship between conductance co-regulation and phase maintenance in STG neurons.     

Correlated Conductance Parameters in Leech Heart Motor Neurons Contribute to Motor Pattern Formation

Neurons can have widely differing intrinsic membrane properties, in particular the density of specific conductances, but how these contribute to characteristic neuronal activity or pattern formation is not well understood. To explore the relationship between conductances, and in particular how they influence the activity of motor neurons in the well characterized leech heartbeat system, we developed a new multi-compartmental Hodgkin-Huxley style leech heart motor neuron model. To do so, we evolved a population of model instances, which differed in the density of specific conductances, capable of achieving specific output activity targets given an associated input pattern. We then examined the sensitivity of measures of output activity to conductances and how the model instances responded to hyperpolarizing current injections. We found that the strengths of many conductances, including those with differing dynamics, had strong partial correlations and that these relationships appeared to be linked by their influence on heart motor neuron activity. Conductances that had positive correlations opposed one another and had the opposite effects on activity metrics when perturbed whereas conductances that had negative correlations could compensate for one another and had similar effects on activity metrics.     

A compartmental model of an external urethral sphincter motoneuron of Onuf's nucleus

This article discusses a model of the electrical behavior of an external urethral sphincter motoneuron, based on morphological parameters like soma size, dendritic diameters and spatial dendritic configuration, and several electrical parameters. Because experimental data about the exact ion conductance mix of external urethral sphincter neurons is scarce, the gaps in knowledge about external urethral sphincter motoneurons were filled in with known data of alpha-motoneurons. The constructed compartmental model of motoneurons of Onuf's nucleus contains six voltage-dependent ionic conductances: a fast sodium and potassium conductance and an anomalous rectifier in the soma; a fast delayed rectifier type potassium conductance and a fast sodium conductance in the initial axon segment; an L-type calcium channel in the dendritic compartments. This paper considers the simulation of external urethral sphincter motoneuron responses to current injections that evoke bistable behavior. Simulations show self-sustained discharge following a depolarizing pulse through the microelectrode; the firing was subsequently terminated by a short hyperpolarizing pulse. This behavior is highly functional for neurons that have to exhibit prolonged activation during sphincter closure. In addition to these 'on' and 'off ' responses, we also observed a particular firing behavior in response to long-lasting triangular current pulses. When the depolarizing current was slowly increased and then decreased (triangular pulse) the firing frequency was higher during the descending phase than during the initial ascending phase.     

Voltage‐sensitive calcium currents and their role in regulating phrenic motoneuron electrical excitability during the perinatal period

This study examined the ontogeny of voltage‐sensitive calcium conductances in rat phrenic motoneurons (PMNs) and their role in regulating electrical excitability during the perinatal period. Specifically, we studied the period spanning from embryonic day (E)16 through postnatal day (P)1, when PMNs undergo fundamental transformation in their morphology, passive properties, ionic channel composition, synaptic inputs, and electrical excitability. Low voltage‐activated (LVA) and high voltage‐activated (HVA) conductances were measured using whole cell patch recordings utilizing a cervical slice‐phrenic nerve preparation from perinatal rats. Changes between E16 and P0–1 included the following: an ≈2‐fold increase in the density of total calcium conductances, an ≈2‐fold decrease in the density of LVA calcium conductances, and an ≈3‐fold increase in the density of HVA conductances. The elevated expression of T‐type calcium channels during the embryonic period lengthened the action potential and enhanced electrical excitability as evidenced by a hyperpolarization‐evoked rebound depolarization. The reduction of LVA current density coupled to the presence of a hyperpolarizing outward A‐type potassium current had a critical effect in diminishing the rebound depolarization in neonatal PMNs. The increase in HVA current density was concomitant with the emergence of a calcium‐dependent “hump‐like” afterdepolarization (ADP) and burst‐like firing. Neonatal PMNs develop a prominent medium‐duration afterhyperpolarization (mAHP) as the result of coupling between N‐type calcium channels and small conductance, calcium‐activated potassium channels. These data demonstrate that changes in calcium channel expression contribute to the maturation of PMN electrophysiological properties during the time from the commencement of fetal inspiratory drive to the onset of continuous breathing at birth. © 2001 John Wiley & Sons, Inc. J Neurobiol 46: 231–248, 2001     

The role of calcium and potassium conductance in electrogenesis of smooth-muscle cells of the basilar artery

The role of calcium and potassium conductances in electrogenesis of smooth muscle cells of the bovine basilar artery has been investigated using blocking agents of calcium and potassium channels both in the normal Krebs solution and in hyperpotassium solution under anelectrotonic repolarization of the cell membrane. It is shown that both voltage-operated calcium and potassium conductances participate in generation of gradual action potentials evoked by electrical stimulation. A higher contribution of potassium conductance into the total membrane conductance during depolarization is found to be the main factor interfered with development of full-size action potential.     

Modulation of Cl-, K+, and nonselective cation conductances by taurine in olfactory receptor neurons of the mudpuppy Necturus maculosus

Odors are transduced by processes that modulate the membrane conductance of olfactory receptor neurons. Olfactory neurons from the aquatic salamander, Necturus maculosus, were acutely isolated without enzymes and studied with a resistive whole-cell method to minimize loss of soluble intracellular constituents. 55 of 224 neurons responded to the test compound taurine at concentrations between 10 nM and 100 microM. Four different conductance changes were elicited by taurine: an increased Cl- conductance (33%), an increased nonselective cation conductance (15%), a decreased Cl- conductance (15%), and a decreased K+ conductance (15%); in addition, responses too small to be characterized were elicited in some neurons. In most cases, taurine appeared to modulate only a single conductance in any particular cell. Modulation of each conductance was dose dependent, and each response ran down quickly in the normal whole-cell mode, presumably due to washout of a diffusible component in the transduction pathway. Modulation of taurine-sensitive conductances caused either inhibitory or excitatory responses. A similar diversity of responses in vivo would produce a complex pattern of electrical activity that could encode the identity and characteristics of an odor.     

Identifying Crucial Parameter Correlations Maintaining Bursting Activity

Recent experimental and computational studies suggest that linearly correlated sets of parameters (intrinsic and synaptic properties of neurons) allow central pattern-generating networks to produce and maintain their rhythmic activity regardless of changing internal and external conditions. To determine the role of correlated conductances in the robust maintenance of functional bursting activity, we used our existing database of half-center oscillator (HCO) model instances of the leech heartbeat CPG. From the database, we identified functional activity groups of burster (isolated neuron) and half-center oscillator model instances and realistic subgroups of each that showed burst characteristics (principally period and spike frequency) similar to the animal. To find linear correlations among the conductance parameters maintaining functional leech bursting activity, we applied Principal Component Analysis (PCA) to each of these four groups. PCA identified a set of three maximal conductances (leak current, _Leak; a persistent K current, _K2; and of a persistent Na+ current, _P) that correlate linearly for the two groups of burster instances but not for the HCO groups. Visualizations of HCO instances in a reduced space suggested that there might be non-linear relationships between these parameters for these instances. Experimental studies have shown that period is a key attribute influenced by modulatory inputs and temperature variations in heart interneurons. Thus, we explored the sensitivity of period to changes in maximal conductances of _Leak, _K2, and _P, and we found that for our realistic bursters the effect of these parameters on period could not be assessed because when varied individually bursting activity was not maintained.     

ATP-sensitive potassium channel and bursting in the pancreatic beta cell. A theoretical study.

Based on the existence of ATP-sensitive potassium channels in the plasma membrane of pancreatic beta cells, we develop a quantitative explanation of the electrical activity observed in pancreatic islets. The proposed mechanism involves the voltage-dependent inward calcium and outward potassium currents described by Rorsman and Trube (1986), which are voltage-activated when an increase in the cytoplasmic ATP/ADP ratio decreases the conductance of the ATP-sensitive potassium channels. It is proposed that modulation of the ATP/ADP ratio occurs through calcium inhibition of oxidative phosphorylation. In this picture the mitochondria serve as a transducer of metabolic activity whose sensitivity is modulated by cytosolic calcium. Solution of the differential equations that describe this mechanism gives rise to both bursting and continuous spiking electrical activity similar to that observed experimentally. While the mechanism for bursting in this model involves the ATP/ADP ratio, the feedback is still provided by calcium, as originally proposed by Chay and Keizer (1983) using a Ca2+-activated potassium conductance. A mixed-model, which includes both ATP-sensitive and Ca2+-activated potassium conductances, also reproduces the experimentally observed electrical activity and may correspond more closely to the actual situation in vivo.     

Single-channel recordings from the apical membrane of the toad urinary bladder epithelial cell

Summary The patch-clamp technique for the recording of single-channel currents was used to investigate the activity of ion channels in the intact epithelium of the toad urinary bladder. High resistance seals were obtained from the apical membrane of tightly stretched tissue. Single-channel recordings revealed the activity of a variety of ion channels that could be classified in 4 groups according to their mean ion conductances, ranging from 5 to 59 pS. In particular, we observed highly selective, amiloridesensitive Na channels with a mean conductance of 4.8 pS, channels with a similar conductance that were not Na-selective and channels with mean conductance values of 17–58 pS that were mostly seen after stimulation of the tissue with vasopressin or cAMP. When inside-out patches from the apical membrane were exposed to 110mm fluoride, large conductances (86–490 pS) appeared.     

Ionic basis for excitability of normal rat kidney (NRK) fibroblasts

Ionic membrane conductances of normal rat kidney (NRK) fibroblasts were characterized by whole-cell voltage-clamp experiments on single cells and small cell clusters and their role in action potential firing in these cells and in monolayers was studied in current-clamp experiments. Activation of an L-type calcium conductance (GCaL) is responsible for the initiation of an action potential, a calcium-activated chloride conductance (GCl(Ca)) determines the plateau phase of the action potential, and an inwardly rectifying potassium conductance (GKir) is important for the generation of a resting potential of approximately -70 mV and contributes to action potential depolarization and repolarization. The unique property of the excitability mechanism is that it not only includes voltage-activated conductances (GCaL, GKir) but that the intracellular calcium dynamics is also an essential part of it (via GCl(Ca)). Excitability was found to be an intrinsic property of a fraction (approximately 25%) of the individual cells, and not necessarily dependent on gap junctional coupling of the cells in a monolayer. Electrical coupling of a patched cell to neighbor cells in a small cluster improved the excitability because all small clusters were excitable. Furthermore, cells coupled in a confluent monolayer produced broader action potentials. Thus, electrical coupling in NRK cells does not merely serve passive conduction of stereotyped action potentials, but also seems to play a role in shaping the action potential.     

Voltage-sensitive calcium currents and their role in regulating phrenic motoneuron electrical excitability during the perinatal period

This study examined the ontogeny of voltage-sensitive calcium conductances in rat phrenic motoneurons (PMNs) and their role in regulating electrical excitability during the perinatal period. Specifically, we studied the period spanning from embryonic day (E)16 through postnatal day (P)1, when PMNs undergo fundamental transformation in their morphology, passive properties, ionic channel composition, synaptic inputs, and electrical excitability. Low voltage-activated (LVA) and high voltage-activated (HVA) conductances were measured using whole cell patch recordings utilizing a cervical slice-phrenic nerve preparation from perinatal rats. Changes between E16 and P0-1 included the following: an approximately 2-fold increase in the density of total calcium conductances, an approximately 2-fold decrease in the density of LVA calcium conductances, and an approximately 3-fold increase in the density of HVA conductances. The elevated expression of T-type calcium channels during the embryonic period lengthened the action potential and enhanced electrical excitability as evidenced by a hyperpolarization-evoked rebound depolarization. The reduction of LVA current density coupled to the presence of a hyperpolarizing outward A-type potassium current had a critical effect in diminishing the rebound depolarization in neonatal PMNs. The increase in HVA current density was concomitant with the emergence of a calcium-dependent "hump-like" afterdepolarization (ADP) and burst-like firing. Neonatal PMNs develop a prominent medium-duration afterhyperpolarization (mAHP) as the result of coupling between N-type calcium channels and small conductance, calcium-activated potassium channels. These data demonstrate that changes in calcium channel expression contribute to the maturation of PMN electrophysiological properties during the time from the commencement of fetal inspiratory drive to the onset of continuous breathing at birth.     

A steady-state model of spreading depression predicts the importance of an unknown conductance in specific dendritic domains

Spreading depression (SD) is a pathological wave of transient neuronal inactivation. We recently reported that the characteristic sustained complete depolarization is restricted to specific cell domains where the input resistance (R(in)) first becomes negligible before achieving partial recovery, whereas in adjacent, more polarized membranes it drops by much less. The experimental study of the participating membrane channels is hindered by their mixed contribution and heterogeneous distribution. Therefore, we derived a biophysical model to analyze the conductances that replicate the subcellular profile of R(in) during SD. Systematic variation of conductance densities far beyond the ranges reported failed to fit the experimental values. Besides standard potassium, sodium, and Glu-mediated conductances, the initial opening and gradual closing of an as yet undetermined large conductance is required to account for the evolution of R(in). Potassium conductances follow in the relative contribution and their closing during the late phase is also predicted. Large intracellular potential gradients from zero to rest are readily sustained between shunted and adjacent SD-spared membranes, which remain electroregenerative. The gradients are achieved by a combination of high-conductance subcellular domains and transmembrane ion redistribution in extended but discrete dendritic domains. We conclude that the heterogeneous subcellular behavior is due to local membrane properties, some of which may be specifically activated under extreme SD conditions.     

Using Multi-Compartment Ensemble Modeling As an Investigative Tool of Spatially Distributed Biophysical Balances: Application to Hippocampal Oriens-Lacunosum/Moleculare (O-LM) Cells

Multi-compartmental models of neurons provide insight into the complex, integrative properties of dendrites. Because it is not feasible to experimentally determine the exact density and kinetics of each channel type in every neuronal compartment, an essential goal in developing models is to help characterize these properties. To address biological variability inherent in a given neuronal type, there has been a shift away from using hand-tuned models towards using ensembles or populations of models. In collectively capturing a neuron''s output, ensemble modeling approaches uncover important conductance balances that control neuronal dynamics. However, conductances are never entirely known for a given neuron class in terms of its types, densities, kinetics and distributions. Thus, any multi-compartment model will always be incomplete. In this work, our main goal is to use ensemble modeling as an investigative tool of a neuron''s biophysical balances, where the cycling between experiment and model is a design criterion from the start. We consider oriens-lacunosum/moleculare (O-LM) interneurons, a prominent interneuron subtype that plays an essential gating role of information flow in hippocampus. O-LM cells express the hyperpolarization-activated current (I _h). Although dendritic I _h could have a major influence on the integrative properties of O-LM cells, the compartmental distribution of I _h on O-LM dendrites is not known. Using a high-performance computing cluster, we generated a database of models that included those with or without dendritic I _h. A range of conductance values for nine different conductance types were used, and different morphologies explored. Models were quantified and ranked based on minimal error compared to a dataset of O-LM cell electrophysiological properties. Co-regulatory balances between conductances were revealed, two of which were dependent on the presence of dendritic I _h. These findings inform future experiments that differentiate between somatic and dendritic I _h, thereby continuing a cycle between model and experiment.     

Role of Calcium Electrogenesis in Apical Dendrites: Generation of Intrinsic Oscillations by an Axial Current

Dendrites are covered with conductances whose function is still mysterious. Using intracellular recording and calcium imaging, we describe an electrogenic band of calcium channels in distal apical dendrites of layer 5 pyramidal neurons (Yuste et al., 1994). We now explore the functional consequences of this distal electrogenic area with multicompartmental numerical simulations. A calcium imaging and electrophysiological database from a single neuron, recorded under blocked sodium and potassium conductances, is replicated by simulations having increased dendritic calcium current. In these models a significant axial current flows from the apical dendrite into the somatic region, activating low-threshold calcium channels and generating oscillations similar to those seen in the electrophysiological data. We propose that the distal electrogenic area in apical dendrites serves to inject current into the soma and produce intrinsic oscillatory dynamics.     

Electrophysiological properties of macrophages

Electrophysiological studies indicate that the macrophage can display at least two different K conductances, a Ca-mediated K conductance and an inward rectifying K conductance, as well as an electrogenic Na+-K+ pump. Spontaneous hyperpolarizations associated with a Ca-mediated K permeability have been noted in all types of macrophages studied. Similar membrane hyperpolarizations can be elicited by a variety of stimuli that presumably increase intracellular calcium. These include mechanical and electrical stimulation as well as exposure to endotoxin-activated serum, chemotactic peptides, and the Ca ionophore A23187. Recent patch clamp studies on macrophages demonstrated channel activity that probably corresponds to currents through the inward rectifying K conductance previously described with current clamp techniques. With the advent of the patch clamp, this and other conductances can be effectively examined by using both whole-cell voltage clamp and patch recordings in a variety of different macrophages, including small freshly isolated cells.     

Comparing ion conductance recordings of synthetic lipid bilayers with cell membranes containing TRP channels

In this article we compare electrical conductance events from single channel recordings of three TRP channel proteins (TRPA1, TRPM2 and TRPM8) expressed in human embryonic kidney cells with channel events recorded on synthetic lipid membranes close to melting transitions. Ion channels from the TRP family are involved in a variety of sensory processes including thermo- and mechano-reception. Synthetic lipid membranes close to phase transitions display channel-like events that respond to stimuli related to changes in intensive thermodynamic variables such as pressure and temperature. TRP channel activity is characterized by typical patterns of current events dependent on the type of protein expressed. Synthetic lipid bilayers show a wide spectrum of electrical phenomena that are considered typical for the activity of protein ion channels. We find unitary currents, burst behavior, flickering, multistep-conductances, and spikes behavior in both preparations. Moreover, we report conductances and lifetimes for lipid channels as described for protein channels. Non-linear and asymmetric current–voltage relationships are seen in both systems. Without further knowledge of the recording conditions, no easy decision can be made whether short current traces originate from a channel protein or from a pure lipid membrane.     

Inhibition of electrical coupling in pairs of murine pancreatic acinar cells by OAG and isolated protein kinase C

Summary Gap junctional coupling was studied in pairs of murine pancreatic acinar cells using the double whole-cell patch-clamp technique. During stable electrical coupling, addition of OAG (1-oleoyl-2-acetyl-sn-glycerol) induced a progressive reduction of the junctional conductance to the detectable limit (3 pS). Prior to complete electrical uncoupling, varius discrete single channel conductances between 20 and 100 pS could be observed. Polymyxin B, a potent inhibitor of the protein kinase C (PKC) system, completely suppressed OAG-stimulated electrical uncoupling. Dialysis of cell pairs with solutions containing PKC. isolated from rat brain, also caused electrical uncoupling. The presence of 0.1mm dibutyryl cyclic AMP and 5mm ATP in the pipette solution, which serves to stabilize the junctional conductance, did not suppress the effects of OAG or isolated PKC. We conclude that an increase of protein kinase C activity leads to the closure of gap junction channels, presumably via a PKC-dependent phosphorylation of the junctional peptide, and that this mechanism is dominant over cAMP-dependent upregulatory effects in the experimental time range (1 hr). A correlation of the observed single channel conductances with the appearance of channel subconductance states or various channel populations is discussed.     

Regulation of murine airway surface liquid volume by CFTR and Ca2+-activated Cl- conductances

Two Cl(-) conductances have been described in the apical membrane of both human and murine proximal airway epithelia that are thought to play predominant roles in airway hydration: (1) CFTR, which is cAMP regulated and (2) the Ca(2+)-activated Cl(-) conductance (CaCC) whose molecular identity is uncertain. In addition to second messenger regulation, cross talk between these two channels may also exist and, whereas CFTR is absent or defective in cystic fibrosis (CF) airways, CaCC is preserved, and may even be up-regulated. Increased CaCC activity in CF airways is controversial. Hence, we have investigated the effects of CFTR on CaCC activity and have also assessed the relative contributions of these two conductances to airway surface liquid (ASL) height (volume) in murine tracheal epithelia. We find that CaCC is up-regulated in intact murine CF tracheal epithelia, which leads to an increase in UTP-mediated Cl(-)/volume secretion. This up-regulation is dependent on cell polarity and is lost in nonpolarized epithelia. We find no role for an increased electrical driving force in CaCC up-regulation but do find an increased Ca(2+) signal in response to mucosal nucleotides that may contribute to the increased Cl(-)/volume secretion seen in intact epithelia. CFTR plays a critical role in maintaining ASL height under basal conditions and accordingly, ASL height is reduced in CF epithelia. In contrast, CaCC does not appear to significantly affect basal ASL height, but does appear to be important in regulating ASL height in response to released agonists (e.g., mucosal nucleotides). We conclude that both CaCC and the Ca(2+) signal are increased in CF airway epithelia, and that they contribute to acute but not basal regulation of ASL height.     

Dendritic spikes and activity-dependent synaptic plasticity

Whereas the regenerative nature of action potential conduction in axons has been known since the late 1940s, neuronal dendrites have been considered as passive cables transferring incoming synaptic activity to the soma. The relatively recent discovery that neuronal dendrites contain active conductances has revolutionized our view of information processing in neurons. In many neuronal cell types, sodium action potentials initiated at the axon initial segment can back-propagate actively into the dendrite thereby serving, for the dendrite, as an indicator of the output activity of the neuron. In addition, the dendrites themselves can initiate action-potential-like regenerative responses, so-called dendritic spikes, that are mediated either by the activation of sodium, calcium, and/or N-methyl-D-aspartate receptor channels. Here, we review the recent experimental and theoretical evidence for a role of regenerative dendritic activity in information processing within neurons and, especially, in activity-dependent synaptic plasticity.