The role of the potassium inward rectifier in defining cell membrane potentials in low potassium media, analysed by computer simulation

A dynamics model of neuron-astrocyte network accounting for febrile seizures

Febrile seizure (FS) is a full-body convulsion caused by a high body temperature that affect young kids, however, how these most common of human seizures are generated by fever has not been known. One common observation is that cortical neurons become overexcited with abnormal running of sodium and potassium ions cross membrane in raised body temperature condition, Considering that astrocyte Kir4.1 channel play a critical role in maintaining extracellular homeostasis of ionic concentrations and electrochemical potentials of neurons by fast depletion of extracellular potassium ions, we examined here the potential role of temperature-dependent Kir4.1 channel in astrocytes in causing FS. We first built up a temperature-dependent computational model of the Kir4.1 channel in astrocytes and validated with experiments. We have then built up a neuron-astrocyte network and examine the role of the Kir4.1 channel in modulating neuronal firing dynamics as temperature increase. The numerical experiment demonstrated that the Kir4.1 channel function optimally in the body temperature around 37 °C in cleaning 'excessive' extracellular potassium ions during neuronal firing process, however, higher temperature deteriorates its cleaning function, while lower temperature slows down its cleaning efficiency. With the increase of temperature, neurons go through different stages of spiking dynamics from spontaneous slow oscillations, to tonic spiking, fast bursting oscillations, and eventually epileptic bursting. Thus, our study may provide a potential new mechanism that febrile seizures may be happened due to temperature-dependent functional disorders of Kir4.1 channel in astrocytes.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11571-021-09706-w.

Myelinating satellite oligodendrocytes are integrated in a glial syncytium constraining neuronal high-frequency activity

Satellite oligodendrocytes (s-OLs) are closely apposed to the soma of neocortical layer 5 pyramidal neurons but their properties and functional roles remain unresolved. Here we show that s-OLs form compact myelin and action potentials of the host neuron evoke precisely timed Ba²⁺-sensitive K⁺ inward rectifying (Kir) currents in the s-OL. Unexpectedly, the glial K⁺ inward current does not require oligodendrocytic Kir4.1. Action potential-evoked Kir currents are in part mediated by gap–junction coupling with neighbouring OLs and astrocytes that form a syncytium around the pyramidal cell body. Computational modelling predicts that glial Kir constrains the perisomatic [K⁺]_o increase most importantly during high-frequency action potentials. Consistent with these predictions neurons with s-OLs showed a reduced probability for action potential burst firing during [K⁺]_o elevations. These data suggest that s-OLs are integrated into a glial syncytium for the millisecond rapid K⁺ uptake limiting activity-dependent [K⁺]_o increase in the perisomatic neuron domain.

Satellite oligodendrocytes (s-OLs) are characterised by their close proximity to neocortical pyramidal cells. Here, the authors find that s-OLs myelinate axons and activity of host neurons evokes inward K⁺ currents in s-OLs which may work to modulate action potential burst firing by buffering extracellular K⁺ levels.

The neuroglial potassium cycle during neurotransmission: role of Kir4.1 channels

Neuronal excitability relies on inward sodium and outward potassium fluxes during action potentials. To prevent neuronal hyperexcitability, potassium ions have to be taken up quickly. However, the dynamics of the activity-dependent potassium fluxes and the molecular pathways underlying extracellular potassium homeostasis remain elusive. To decipher the specific and acute contribution of astroglial Kir4.1 channels in controlling potassium homeostasis and the moment to moment neurotransmission, we built a tri-compartment model accounting for potassium dynamics between neurons, astrocytes and the extracellular space. We here demonstrate that astroglial Kir4.1 channels are sufficient to account for the slow membrane depolarization of hippocampal astrocytes and crucially contribute to extracellular potassium clearance during basal and high activity. By quantifying the dynamics of potassium levels in neuron-glia-extracellular space compartments, we show that astrocytes buffer within 6 to 9 seconds more than 80% of the potassium released by neurons in response to basal, repetitive and tetanic stimulations. Astroglial Kir4.1 channels directly lead to recovery of basal extracellular potassium levels and neuronal excitability, especially during repetitive stimulation, thereby preventing the generation of epileptiform activity. Remarkably, we also show that Kir4.1 channels strongly regulate neuronal excitability for slow 3 to 10 Hz rhythmic activity resulting from probabilistic firing activity induced by sub-firing stimulation coupled to Brownian noise. Altogether, these data suggest that astroglial Kir4.1 channels are crucially involved in extracellular potassium homeostasis regulating theta rhythmic activity.

Electrical coupling in ensembles of nonexcitable cells: modeling the spatial map of single cell potentials

We analyze the coupling of model nonexcitable (non-neural) cells assuming that the cell membrane potential is the basic individual property. We obtain this potential on the basis of the inward and outward rectifying voltage-gated channels characteristic of cell membranes. We concentrate on the electrical coupling of a cell ensemble rather than on the biochemical and mechanical characteristics of the individual cells, obtain the map of single cell potentials using simple assumptions, and suggest procedures to collectively modify this spatial map. The response of the cell ensemble to an external perturbation and the consequences of cell isolation, heterogeneity, and ensemble size are also analyzed. The results suggest that simple coupling mechanisms can be significant for the biophysical chemistry of model biomolecular ensembles. In particular, the spatiotemporal map of single cell potentials should be relevant for the uptake and distribution of charged nanoparticles over model cell ensembles and the collective properties of droplet networks incorporating protein ion channels inserted in lipid bilayers.

Membrane potential bistability in nonexcitable cells as described by inward and outward voltage-gated ion channels

The membrane potential of nonexcitable cells, defined as the electrical potential difference between the cell cytoplasm and the extracellular environment when the current is zero, is controlled by the individual electrical conductance of different ion channels. In particular, inward- and outward-rectifying voltage-gated channels are crucial for cell hyperpolarization/depolarization processes, being amenable to direct physical study. High (in absolute value) negative membrane potentials are characteristic of terminally differentiated cells, while low membrane potentials are found in relatively depolarized, more plastic cells (e.g., stem, embryonic, and cancer cells). We study theoretically the hyperpolarized and depolarized values of the membrane potential, as well as the possibility to obtain a bistability behavior, using simplified models for the ion channels that regulate this potential. The bistability regions, which are defined in the multidimensional state space determining the cell state, can be relevant for the understanding of the different model cell states and the transitions between them, which are triggered by changes in the external environment.

First order phase transition and hysteresis in a cell's maintenance of the membrane potential--An essential role for the inward potassium rectifiers

Hysteretic behavior is found experimentally in the transmembrane potential at low extracellular potassium in mouse lumbrical muscle cells. Adding isoprenaline to the external medium eliminates the bistable, hysteretic region. The system can be modeled mathematically and understood analytically with and without isoprenaline. Inward rectifying potassium channels appear to be essential for the bistability. Relations are derived to express the dimensions of the bistable area in terms of system parameters. The selective advantage and evolutionary origin of inward rectifying channels and hysteretic behavior is discussed.

Computer simulations of neuron-glia interactions mediated by ion flux

Extracellular potassium concentration, [K(+)](o), and intracellular calcium, [Ca(2+)](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(+), Ca(2+) 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.

A bistable membrane potential at low extracellular potassium concentration

In order to understand the electrochemical behavior of a living cell at a low extracellular potassium concentration, a model is constructed. The model involves only the ATP driven sodium-potassium pump, and the sodium and potassium channels. Predictions of the model fit the N-shape of the current-voltage characteristic at low extracellular potassium. The model can, furthermore, quantitatively account for the experimentally observed bistability of the membrane potential at low extracellular potassium concentration. A crucial role in the control of the transmembrane potential appears to be played by how the permeability of the inward rectifying potassium channels depends on the transmembrane potential and on the extracellular potassium concentration.

Isoprenaline-stimulated differential adrenergic response of K+ channels in skeletal muscle under hypokalaemic conditions

The mechanism underlying the hyperpolarization induced by isoprenaline in mouse lumbrical muscle fibres was studied using cell-attached patch and intracellular membrane potential ( V(m)) recordings. Sarcolemmal inwardly rectifying K(+) channels (K(IR): 45 pS) and Ca(2+)-activated K(+) channels (BK: 181 pS) were identified. Exposure to isoprenaline closed K(IR) channels and increased BK channel activity. This increase was observed as a shift from 50 to -40 mV in the voltage dependence of channel activation. Isoprenaline prevented hysteresis of V(m) when the extracellular [K(+)] fell below 3.8 mM. This hysteresis was due to the properties of the K(IR). The effects of chloride transport and isoprenaline on V(m) did not interact purely competitively, but isoprenaline could prevent the depolarization induced by hyperosmotic media equally as well as bumetanide, which inhibits the Na(+)/K(+)/2Cl(-) cotransporter. In lumbrical muscle this leads to hyperpolarization, but this might vary among muscles. The switch from K(IR) to BK as the component of total K(+) conductance was due to isoprenaline.

Effects of chloride transport on bistable behaviour of the membrane potential in mouse skeletal muscle

The lumbrical skeletal muscle fibres of mice exhibited electrically bistable behaviour due to the nonlinear properties of the inwardly rectifying potassium conductance. When the membrane potential (V(m)) was measured continuously using intracellular microelectrodes, either a depolarization or a hyperpolarization was observed following reduction of the extracellular potassium concentration (K+o) from 5.7 mM to values in the range 0.76-3.8 mM, and V(m) showed hysteresis when K+o was slowly decreased and then increased within this range. Hypertonicity caused membrane depolarization by enhancing chloride import through the Na+-K+-2Cl- cotransporter and altered the bistable behaviour of the muscle fibres. Addition of bumetanide, a potent inhibitor of the Na+-K+-2Cl- cotransporter, and of anthracene-9-carboxylic acid, a blocker of chloride channels, caused membrane hyperpolarization particularly under hypertonic conditions, and also altered the bistable behaviour of the cells. Hysteresis loops shifted with hypertonicity to higher K+o values and with bumetanide to lower values. The addition of 80 microM BaCl2 or temperature reduction from 35 to 27 degrees C induced a depolarization of cells that were originally hyperpolarized. In the K+o range of 5.7-22.8 mM, cells in isotonic media (289 mmol x kg(-1)) responded nearly Nernstianly to K+o reduction, i.e. 50 mV per decade; in hypertonic media this dependence was reduced to 36 mV per decade (319 mmol x kg(-1)) or to 31 mV per decade (340 mmol x kg(-1)). Our data can explain apparent discrepancies in DeltaV(m) found in the literature. We conclude that chloride import through the Na+-K+-2Cl- cotransporter and export through Cl- channels influenced the V(m) and the bistable behaviour of mammalian skeletal muscle cells. The possible implication of this bistable behaviour in hypokalaemic periodic paralysis is discussed.

Osmolality influences bistability of membrane potential under hypokalemic conditions in mouse skeletal muscle: an experimental and theoretical study

The membrane potential in mouse skeletal muscle depends on both extracellular osmolality and potassium concentration. These dependencies have been related to two membrane transporters, Na+/K+/2Cl- co-transporter and the inward potassium rectifier channel. To investigate the relation of the Na+/K+/2Cl- co-transporter and the inward potassium rectifier channel in a qualitative way, a combined electrophysiological and modelling approach was used. The experimental results show that the bistability of the membrane potential, which is related to the conductive state of the inward potassium rectifier channel, is shifted to higher extracellular potassium values when medium osmolality is increased. These results are confirmed by the computer simulation calculations for increased co-transporter flux. The combined results indicate that the co-transporter is capable of modulating the conductive state of the inward potassium rectifier channel.

Dynamics and consequences of potassium shifts in skeletal muscle and heart during exercise

Since it became clear that K(+) shifts with exercise are extensive and can cause more than a doubling of the extracellular [K(+)] ([K(+)](s)) as reviewed here, it has been suggested that these shifts may cause fatigue through the effect on muscle excitability and action potentials (AP). The cause of the K(+) shifts is a transient or long-lasting mismatch between outward repolarizing K(+) currents and K(+) influx carried by the Na(+)-K(+) pump. Several factors modify the effect of raised [K(+)](s) during exercise on membrane potential (E(m)) and force production. 1) Membrane conductance to K(+) is variable and controlled by various K(+) channels. Low relative K(+) conductance will reduce the contribution of [K(+)](s) to the E(m). In addition, high Cl(-) conductance may stabilize the E(m) during brief periods of large K(+) shifts. 2) The Na(+)-K(+) pump contributes with a hyperpolarizing current. 3) Cell swelling accompanies muscle contractions especially in fast-twitch muscle, although little in the heart. This will contribute considerably to the lowering of intracellular [K(+)] ([K(+)](c)) and will attenuate the exercise-induced rise of intracellular [Na(+)] ([Na(+)](c)). 4) The rise of [Na(+)](c) is sufficient to activate the Na(+)-K(+) pump to completely compensate increased K(+) release in the heart, yet not in skeletal muscle. In skeletal muscle there is strong evidence for control of pump activity not only through hormones, but through a hitherto unidentified mechanism. 5) Ionic shifts within the skeletal muscle t tubules and in the heart in extracellular clefts may markedly affect excitation-contraction coupling. 6) Age and state of training together with nutritional state modify muscle K(+) content and the abundance of Na(+)-K(+) pumps. We conclude that despite modifying factors coming into play during muscle activity, the K(+) shifts with high-intensity exercise may contribute substantially to fatigue in skeletal muscle, whereas in the heart, except during ischemia, the K(+) balance is controlled much more effectively.

Modulation of the isoprenaline-induced membrane hyperpolarization of mouse skeletal muscle cells

1. The hyperpolarization of the resting membrane potential, Vm, induced by isoprenaline in the lumbrical muscle fibres of the mouse, was investigated by use of intracellular microelectrodes. 2. In normal Krebs-Henseleit solution (potassium concentration: K+o = 5.7 mM, 'control'), Vm was -7.40 +/- 0.2 mV; lowering K+o to 0.76 mM ('low K+o') resulted in either a hyperpolarization (Vm = -95.7 +/- 2.9 mV), or a depolarization (Vm = -52.0 +/- 0.3 mV). 3. Isoprenaline (> or = 200 nM) induced a hyperpolarization of Vm by delta Vm = -5.6 +/- 0.4 mV in control solution. 4. When Vm hyperpolarized after switching to low K+o, the addition of isoprenaline resulted in increased hyperpolarization Vm: delta Vm = -16.3 +/- 3.2 mV to a final Vm = -110.1 +/- 3.4 mV. Adding iso-prenaline when Vm depolarized in low K+o, leads to a hyperpolarization of either by -11.6 +/- 0.5 mV to -63.6 +/- 0.8 mV or by -51.7 +/- 2.7 mV to -106.9 +/- 3.9 mV. 5. Ouabain (0.1 to 1 mM) did not suppress the hyperpolarization by isoprenaline in 5.7 mM K+o (delta Vm = -6.7 +/- 0.4 mV) or the hyperpolarization of the depolarized cells in low K+- (delta Vm = -9.7 +/- 1.5 mV). 6. The hyperpolarization is a logarithmically decreasing function of K+o in the range between 2 and 20 mM (12 mV/decade). 7.IBMX and 8Br-cyclic AMP mimicked the response to isoprenaline whereas forskolin (FSK) induced in low K+o a hyperpolarization of -7.0 +/- 0.7 mV that could be augmented by addition of isoprenaline (delta Vm = -8.2 +/- 1.8 mV). 8. In control and low K+o, Ba2+ (0.6 mM) inhibited the hyperpolarization induced by isoprenaline, IBMX or 8Br-cyclic AMP. Other blockers of the potassium conductance such as TEA (5 mM) and apamin (0.4 microM) had no effect. 9. We conclude that in the lumbrical muscle of the mouse the isoprenaline-induced hyperpolarization is primarily due to an increase in potassium permeability.