Sodium channel slow inactivation normalizes firing in axons with uneven conductance distributions

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Effects of a slow potassium permeability on repetitive activity of the frog node of ranvier

Adding a potassium permeability with slow kinetics to the Frankenhaeuser-Huxley equations describing action potential generation at a frog node of Ranvier has a twofold effect on the maintained repetitive firing the model can show. If the contribution of the slow to the total potassium permeability is increased, the maintained discharge frequency for a given stimulating current experiences a decrease. On the other hand, addition of the slow channel narrows the range of currents for which the model can generate repetitive activity. If as little as 6.2% of the total potassium permeability are provided by the slow channels, the Frankenhaeuser-Huxley equations completely lose the ability to show maintained firing. The introduction of the slow potassium current abolishes especially repetitive activity at low values of stimulating current. This effect is so marked that the minimal discharge frequency the model can maintain increases with increasing contribution of the slow channel. Therefore, an important purpose of the slow potassium channel present at the frog nodal membrane could consist of preventing the node of Ranvier from generating consistent firing on its own.     

Ion channel density and threshold dynamics of repetitive firing in a cortical neuron model

Modifying the density and distribution of ion channels in a neuron (by natural up- and down-regulation, by pharmacological intervention or by spontaneous mutations) changes its activity pattern. In the present investigation, we analyze how the impulse patterns are regulated by the density of voltage-gated channels in a model neuron, based on voltage clamp measurements of hippocampal interneurons. At least three distinct oscillatory patterns, associated with three distinct regions in the Na-K channel density plane, were found. A stability analysis showed that the different regions are characterized by saddle-node, double-orbit, and Hopf bifurcation threshold dynamics, respectively. Single strongly graded action potentials occur in an area outside the oscillatory regions, but less graded action potentials occur together with repetitive firing over a considerable range of channel densities. The presently found relationship between channel densities and oscillatory behavior may be relevance for understanding principal spiking patterns of cortical neurons (regular firing and fast spiking). It may also be of relevance for understanding the action of pharmacological compounds on brain oscillatory activity.     

Involvement of calcium-dependent potassium conductance in membrane hyperpolarization processes at the pyramidal cell membrane in the cat sensorimotor cortex

In acute experiments on cats immobilized with myorelaxants intracellular injection of Cs ions reduced IPSP amplitude and postburst hyperpolarization of pyramidal cells in the sensorimotor cortex. Intracellular injection of ethylene glycol tetra-acetic acid produced a similar effect. The latter substance barely altered the lead front of neuronal after-hyperpolarization arising after a single action potential, while the lag front was inhibited. In conclusion, calcium-dependent potassium conductance may play an important part in the genesis of IPSP and of post-burst and after-hyperpolarization at the membrane of pyramidal cells of the cat sensorimotor cortex.I. S. Beritashvili Institute of Physiology, Academy of Sciences of the Georgian SSR, Tbilisi. Translated from Neirofiziologiya, Vol. 20, No. 3, pp. 383–389, May–June, 1988.     

Cross talk between activation and slow inactivation gates of Shaker potassium channels

This study addresses the energetic coupling between the activation and slow inactivation gates of Shaker potassium channels. To track the status of the activation gate in inactivated channels that are nonconducting, we used two functional assays: the accessibility of a cysteine residue engineered into the protein lining the pore cavity (V474C) and the liberation by depolarization of a Cs(+) ion trapped behind the closed activation gate. We determined that the rate of activation gate movement depends on the state of the inactivation gate. A closed inactivation gate favors faster opening and slower closing of the activation gate. We also show that hyperpolarization closes the activation gate long before a channel recovers from inactivation. Because activation and slow inactivation are ubiquitous gating processes in potassium channels, the cross talk between them is likely to be a fundamental factor in controlling ion flux across membranes.     

Regulation of potassium conductance in the cellular membrane at early embryogenesis.

At the early stages of development of the fresh water fish loach (Misgurnus fossilis) the resting membrane potential (Er) of cleaving cells oscillates periodically with an amplitude of 8-12 mV. Er oscillation correlates with the cell cycle and is accompanied by changes of K+ conductivity. Two types of K(+)-selective ionic channels with conductance of approximately 70 and 25 pS in symmetrical (150 mM KCl) solution were observed in the membrane of cleaving loach embryos. 'High' conductance and 'low' conductance channels were recorded in approximately 90% and 10% of patches investigated (n = 275), respectively? The activity of 'high' conductance channels was regulated by the application of pressure to the membrane, ie these channels were stretch-activated (SA). The activity of SA channels changes dramatically during the cell-cleavage cycle. At the beginning of interphase the probability of SA channels being in the open state (P0) was minimal, while at prometaphase the probability was increased 10-100-fold. Application of ATP to the cytoplasmic inside-out patches induced a reversible elevation of stretch sensitivity of the SA channels in 50% of the patches, while the non-hydrolyzable analogue of ATP was not effective. Combined application of ATP, cAMP and cAMP-dependent protein kinase (PK) induced a reversible elevation in the SA channel activity while inhibitors of PK prevented its activating effects. Phosphatase inhibitors prolonged the activating effect of PK on SA channels. We propose that oscillations of the resting potential during the cell-cleavage cycle arise due to modulation of SA channel sensitivity to stretch through cAMP-dependent phosphorylation.     

Dependence of tetanic hyperpolarization on pump conductance in the cyanide-treatedXenopus node

Prolonged exposure to cyanide leads to a delayed but reversible disappearance of tetanic hyperpolarization in theXenopus node (G. M. Schoepfle,Am. J. Physiol. 231, 1033–1038, 1976). This effect is attributed to a pronounced decline in the absolute values of the ATP and ADP concentrations, such that the ATP-driven ion translocation is no longer possible, regardless of the existing values for (Na)_i, (K)_i and the (ATP)/(ADP) ratio. Mathematically, this would imply a vanishing of a constant pump conductance g_p in the exression for electrogenic pump current densitityJ _p, whereJ _p=g _p (V _m −E _p) in whichV _m is membrane potential andE _p is an ATP-and sodium-dependent e.m.f. Supported by NIH grant NS08802.     

Regenerating mammalian nerve fibres: changes in action potential waveform and firing characteristics following blockage of potassium conductance

Extracellular application of potassium channel blocking agents is known to increase the amplitude and duration of the compound action potential in non-myelinated and demyelinated axons, but not in mature mammalian myelinated fibres. In the present study we used intra-axonal and whole nerve recording techniques to study the effects of the potassium channel blocking agent 4-aminopyridine (4-AP) on regenerating rat nerve fibres. Our results indicate that early regenerating (premyelinated) axons show considerable broadening of the action potential after 4-AP application and late regenerating (myelinated) axons give rise to burst activity following a single stimulus after 4-AP application. 4-AP did not affect spike waveform or firing properties of normal mature sciatic nerve fibres. These results demonstrate the importance of potassium conductance in stabilizing firing properties of myelinated regenerating axons.     

Calcium-dependent potassium conductance in the photoresponse of a nudibranch mollusk

• 1.1. The response to light of Hermissenda photoreceptors when recorded intracellularly without interference from synaptic and action potentials consisted of three phases: an early depolarization (ED) followed by hyperpolarization (dip) and subsequent depolarization (tail).
• 2.2. The ED and the dip were associated with increased membrane conductance while decreased membrane conductance was involved with the tail.
• 3.3. The dip reversal potential was − 82.1 ± 5.3 mV and its amplitude varied inversely with the log of [K⁺].
• 4.4. Perfusing with agents which block K⁺ current like 4AP, Quinine, Quinidine or injection of TEA eliminated the dip and its associated increased membrane conductance, thus further supporting the role of K⁺ conductance in producing the dip.
• 5.5. The dip was enhanced by increased [Ca²⁺]_o, reduced by decreased [Ca²⁺]_o and abolished together with its associated increased membrane conductance when perfused with either D600, Cd²⁺, Mg²⁺, Mn²⁺, or Co²⁺, which block transmembrane Ca²⁺ current.
• 6.6. The dip and its associated increased membrane conductance were abolished by intracellular injection of EGTA and enhanced by perfusion with Ruthenium red.
• 7.7. Intracellular injection of Ca²⁺ mimicked the dip: membrane conductance was increased and the cell hyperpolarized.
• 8.8. These results indicate that the increase in intracellular [Ca²⁺] is primarily responsible for the light-induced increase of K⁺ conductance during the dip. The possible source of the Ca²⁺ is, at least in part, extracellular due to activation of an inward Ca²⁺ current.

     

Modeling repetitive firing and bursting in a small unmyelinated nerve fiber.

The Hodgkin-Huxley equations, originally developed to describe the electrical events in the squid giant axon, have been modified to simulate the ionic and electrical events in a small unmyelinated nerve fiber. The modified equations incorporate an electrogenic sodium-potassium pump, finite intra-axonal volume, a periaxonal space, a calcium current, and calcium-dependent potassium conductance (GKCa). The model shows that adaptation can occur in two ways: increased Na-K pump activity because of periaxonal K accumulation or intra-axonal Na accumulation; or from an increase in (GKCa) caused by calcium accumulating within the axon. Bursting is an extension of adaptation and occurs when the sensitivity of the Na-K pump or (GKCa) to changes in ionic concentration is increased.     

Sodium channels: ionic model of slow inactivation and state-dependent drug binding

Inactivation is a fundamental property of voltage-gated ion channels. Fast inactivation of Na(+) channels involves channel block by the III-IV cytoplasmic interdomain linker. The mechanisms of nonfast types of inactivation (intermediate, slow, and ultraslow) are unclear, although the ionic environment and P-loops rearrangement appear to be involved. In this study, we employed a TTX-based P-loop domain model of a sodium channel and the MCM method to investigate a possible role of P-loop rearrangement in the nonfast inactivation. Our modeling predicts that Na(+) ions can bind between neighboring domains in the outer-carboxylates ring EEDD, forming an ordered structure with interdomain contacts that stabilize the conducting conformation of the outer pore. In this model, the permeant ions can transit between the EEDD ring and the selectivity filter ring DEKA, retaining contacts with at least two carboxylates. In the absence of Na(+), the electrostatic repulsion between the EEDD carboxylates disrupts the permeable configuration. In this Na(+)-deficient model, the region between the EEDD and DEKA rings is inaccessible for Na(+) but is accessible for TMA. Taken together, these results suggest that Na(+)-saturated models are consistent with experimental characteristics of the open channels, whereas Na(+)-deficient models are consistent with experimentally defined properties of the slow-inactivated channels. Our calculations further predict that binding of LAs to the inner pore would depend on whether Na(+) occupies the DEKA ring. In the absence of Na(+) in the DEKA ring, the cationic group of lidocaine occurs in the focus of the pore helices' macrodipoles and would prevent occupation of the ring by Na(+). Loading the DEKA ring with Na(+) results in the electrostatic repulsion with lidocaine. Thus, there are antagonistic relations between a cationic ligand bound in the inner pore and Na(+) in the DEKA ring.     

Frequency relations of capacitance and conductance of the system electrolyte--membrane--electrolyte in a model framework]

An electrodiffusion model of immediate permeability of ions through the lipid membrane was considered. The model suggests the existence of finite immovable layers of the electrolyte near the membrane. A technique is given for linearization and obtaining analytical solutions of the time-dependent electrodiffusion equations for one ion species. The expression for admittence of the system was obtained. The model allowed to obtain the curves of c (omega) and g (omega) which agreed with the empiric ones.     

Reciprocal inhibition and slow calcium decay in perigeniculate interneurons explain changes of spontaneous firing of thalamic cells caused by cortical inactivation

The role of cortical feedback in the thalamocortical processing loop has been extensively investigated over the last decades. With an exception of several cases, these searches focused on the cortical feedback exerted onto thalamo-cortical relay (TC) cells of the dorsal lateral geniculate nucleus (LGN). In a previous, physiological study, we showed in the cat visual system that cessation of cortical input, despite decrease of spontaneous activity of TC cells, increased spontaneous firing of their recurrent inhibitory interneurons located in the perigeniculate nucleus (PGN). To identify mechanisms underlying such functional changes we conducted a modeling study in NEURON on several networks of point neurons with varied model parameters, such as membrane properties, synaptic weights and axonal delays. We considered six network topologies of the retino-geniculo-cortical system. All models were robust against changes of axonal delays except for the delay between the LGN feed-forward interneuron and the TC cell. The best representation of physiological results was obtained with models containing reciprocally connected PGN cells driven by the cortex and with relatively slow decay of intracellular calcium. This strongly indicates that the thalamic reticular nucleus plays an essential role in the cortical influence over thalamo-cortical relay cells while the thalamic feed-forward interneurons are not essential in this process. Further, we suggest that the dependence of the activity of PGN cells on the rate of calcium removal can be one of the key factors determining individual cell response to elimination of cortical input.     

Inhibition modifies the effects of slow calcium-activated potassium channels on epileptiform activity in a neuronal network model

Generation of epileptiform activity typically results from a change in the balance between network excitation and inhibition. Experimental evidence indicates that alterations of either synaptic activity or intrinsic membrane properties can produce increased network excitation. The slow Ca²⁺-activated K⁺ currents (sI_AHP) are important modulators of neuronal firing rate and excitability and have important established and potential roles in epileptogenesis. While the effects of changes in sI_AHP on individual neuronal excitability are readily studied and well established, the effects of such changes on network behavior are less well known. The experiments here utilize a defined small network model of multicompartment pyramidal cells and an inhibitory interneuron to study the effects of changes in sI_AHP on network behavior. The benefits of this model system include the ability to observe activity in all cells in a network and the effects of interactions of multiple simultaneous influences. In the model with no inhibitory interneuron, increasing sI_AHP results in progressively decreasing burst activity. Adding an inhibitory interneuron changes the observed effects; at modest inhibitory strengths, increasing sI_AHP in all network neurons actually results in increased network bursting (except at very high values). The duration of the burst activity is influenced by the length of delay in a feedback loop, with longer loops resulting in more prolonged bursting. These observations illustrate that the study of potential antiepileptogenic membrane effects must be extended to realistic networks. Network inhibition can dramatically alter the observations seen in pure excitatory networks.     

Excitability of single firing human motoneurones to single and repetitive stimulation (experiment and model)

The activity of single motoneurones of m. flexor carpi ulnaris (FCU) was investigated by recording their motor unit (MU) action potentials during weak and moderate voluntary muscle contractions. The MU firing rate range was 4.5-15 imp/s. The excitability of motoneurones was tested with a number of single stimuli eliciting a monosynaptic H-reflex of low amplitude. Two different indices were defined which relate to motoneuronal excitability: the response index--the ratio of the number of responses of a motoneurone to the total number of stimuli, and the response time--the time after the last background MU discharge at which motoneurone is ready to respond to the excitatory volley. Both the response index and the response time were determined for single motoneurones at different levels of background activity. In the lower range of firing rates, the response index for all motoneurones decreased when increasing the firing rate, but it remained constant in the higher rate range. This kind of response seems to be a typical motoneuronal response to the stimulation with single stimuli. The data on the response time were used to study the excitability of the same single motoneurones to computer simulated repetitive stimulation (stimulation rate 40-100 imp/s). In this case, the excitability of each motoneurone was determined as an increment of its firing rate in response to the stimulation. For the lower firing rate range, the excitability for all motoneurones also decreased when the firing rates increased whereas a variety of slopes was obtained in the higher rate range.(ABSTRACT TRUNCATED AT 250 WORDS)     

Epileptogenesis: A model for the involvement of slow membrane events and extracellular potassium

A computer model was developed, based in part on voltage-clamp data from Aplysia bursting pacemaker cells. This model was used to explore the interaction of slow subthreshold membrane properties with the synaptic events and the accumulation of extracellular potassium which are thought to occur in experimental epileptic foci. Results of the model suggest a new role for potassium ions and subthreshold membrane events in epileptogenesis—namely, that an increase in extracellular potassium may transform a group of stable cells into unstable, oscillatory cells, independent of synaptic activity. The model also suggests that a population of cells may be more susceptible than single cells to this transformation.     

Oscillations in stomatal conductance and plant functioning associated with stomatal conductance: Observations and a model

Summary Measurements of transpiration, leaf water content, and flux of water in a cotton plant exhibiting sustained oscillations, in stomatal conductance are presented, and a model of the mechanism causing this behaviour is developed. The dynamic elements, of the model are capacitors—representing the change of water content with water potential in mesophyll, subsidiary and guard cells—interconnected by resistances representing flow paths in the plant. Increase of water potential in guard cells causes an increase in stomatal conductance. Increase of water potential in the subsidiary cells has the opposite effect and provides the positive feed-back which can cause stomatal conductance to oscillate. The oscillations are shown to have many of the characteristics of free-running oscillations in real plants. The behaviour of the model has been examined, using an analogue computer, with constraints and perturbations representing some of those which could be applied to real plants in physiological experiments. Aspects of behaviour which have been simulated are (a) opening and closing of stomata under the influence of changes in illumination, (b) transient responses due to step changes in potential transpiration, root permeability and potential of water surrounding the roots, (c) the influence of these factors on the occurrence and shape of spontaneous oscillations, and (d) modulation of sustained oscillations due to a circadian rhythm in the permeability of roots.