Depolarizing Afterpotential Research Articles

Estradiol directly attenuates sodium currents and depolarizing afterpotentials in isolated gonadotropin-releasing hormone neurons

The gonadotropin-releasing hormone (GnRH) neuron is the pivotal control center in a tightly regulated reproductive axis. The release of GnRH controls estradiol production by the ovary, and estradiol acts at the hypothalamus to regulate GnRH release. However, the mechanisms of estradiol feedback are just beginning to be understood. We have previously shown that estradiol administered to the female mouse modulates sodium currents in fluorescently-labeled GnRH neurons. In the current studies, estradiol (1nM) was applied directly, for 16–24h, to hypothalamic cultures from young or aged female ovariectomized mice. The direct application of estradiol modulated a tetrodotoxin-sensitive sodium current in isolated GnRH neurons from both young and aged animals. Estradiol, and the specific estrogen receptor-β agonist DPN, decreased current amplitude measured in the morning (AM), but had no effect on afternoon currents. These compounds also decreased the rise and decay slope of the current response, increased the width of the current, and increased action potential width in AM recordings. In addition, estradiol decreased the amplitude of the depolarizing afterpotential (DAP); this effect was not time-of-day dependent. The ER-β agonist DPN did not mimic the effect of estradiol on DAPs, and the modulation of DAPs by estradiol was no longer present in cells from postreproductive animals. These results indicate that estradiol can affect the physiology of GnRH neurons via multiple pathways that are differentially regulated during the transition to reproductive senescence, suggesting that estradiol regulation of GnRH neuronal output is modulated during the aging process.

Role of neuronal potassium M-channels in sympathetic regulation of cardiac function

Role of neuronal potassium M-channels in sympathetic regulation of cardiac function

Synaptic activation of mGluR1 generates persistent depression of a fast after-depolarizing potential in CA3 pyramidal neurons

Burst firing is an important property of hippocampal pyramidal neurons. Group I metabotropic glutamate receptors (mGluRs) produce a multitude of effects on both the synaptic and intrinsic properties of neurons. We investigated whether brief activation of these receptors results in persistent modifications to the intrinsic excitability of rat hippocampal CA3 pyramidal cells (CA3-PCs). In whole-cell current-clamp recordings, current stimuli consisting of filtered, pseudo-random noise produced action potential firing with a mean frequency of ∼1.5-2 Hz. Analysis of spike intervals revealed that this firing included a substantial component (∼20%) of high-frequency (∼100 Hz) bursting activity. Activation of group I mGluRs with (S)-3,5-dihydroxyphenylglycine [(S)-DHPG] selectively eliminated the high-frequency bursts, an effect that persisted > 30 min after (S)-DHPG washout. The fast after-depolarizing potential (ADP) of CA3-PCs is known to be important for generating high-frequency action potential bursting. This ADP was persistently depressed following a short application of (S)-DHPG. This effect was blocked by the mGluR1 antagonist, (S)-(+)-α-amino-4-carboxy-2-methylbenzeneacetic acid (LY367385). In contrast, the depression was resistant to the mGluR5 antagonist 2-methyl-6-(phenylethynyl)pyridine hydrochloride (MPEP) and α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)/kainate, N-methyl-D-aspartate (NMDA) and γ-aminobutyric acid (GABA)(A) antagonists. Unlike other manipulations that generate persistent depression of the ADP in CA3-PCs, DHPG-mediated ADP depression was insensitive to the Kv7 channel inhibitor 10,10-bis(4-Pyridinylmethyl)-9(10H)-anthracenone dihydrochloride (XE991) and strong intracellular Ca(2+) buffering by 1,2-Bis(2-aminophenoxy)ethane-N,N,N',N'-tetraacetic acid (BAPTA). Synaptic activation of mGluRs in the associational-commissural pathway also resulted in persistent depression of the ADP in postsynaptic CA3-PCs, which was blocked by LY367385. These data represent the first evidence that synaptic activation of mGluR1 can modulate the intrinsic excitability properties of hippocampal neurons.

Presynaptic Resurgent Na+Currents Sculpt the Action Potential Waveform and Increase Firing Reliability at a CNS Nerve Terminal

Axonal and nerve terminal action potentials often display a depolarizing after potential (DAP). However, the underlying mechanism that generates the DAP, and its impact on firing patterns, are poorly understood at axon terminals. Here, we find that at calyx of Held nerve terminals in the rat auditory brainstem the DAP is blocked by low doses of externally applied TTX or by the internal dialysis of low doses of lidocaine analog QX-314. The DAP is thus generated by a voltage-dependent Na(+) conductance present after the action potential spike. Voltage-clamp recordings from the calyx terminal revealed the expression of a resurgent Na(+) current (I(NaR)), the amplitude of which increased during early postnatal development. The calyx of Held also expresses a persistent Na(+) current (I(NaP)), but measurements of calyx I(NaP) together with computer modeling indicate that the fast deactivation time constant of I(NaP) minimizes its contribution to the DAP. I(NaP) is thus neither sufficient nor necessary to generate the calyx DAP, whereas I(NaR) by itself can generate a prominent DAP. Dialysis of a small peptide fragment of the auxiliary β4 Na(+) channel subunit into immature calyces (postnatal day 5-6) induced an increase in I(NaR) and a larger DAP amplitude, and enhanced the spike-firing precision and reliability of the calyx terminal. Our results thus suggest that an increase of I(NaR) during postnatal synaptic maturation is a critical feature that promotes precise and resilient high-frequency firing.

Hypertension Induced by Angiotensin II and a High Salt Diet Involves Reduced SK Current and Increased Excitability of RVLM Projecting PVN Neurons

Although evidence indicates that activation of presympathetic paraventricular nucleus (PVN) neurons contributes to the pathogenesis of salt-sensitive hypertension, the underlying cellular mechanisms are not fully understood. Recent evidence indicates that small conductance Ca(2+)-activated K(+) (SK) channels play a significant role in regulating the excitability of a key group of sympathetic regulatory PVN neurons, those with axonal projections to the rostral ventrolateral medulla (RVLM; i.e., PVN-RVLM neurons). In the present study, rats consuming a high salt (2% NaCl) diet were made hypertensive by systemic infusion of angiotensin II (AngII), and whole cell patch-clamp recordings were made in brain slice from retrogradely labeled PVN-RVLM neurons. To determine if the amplitude of SK current was altered in neurons from hypertensive rats, voltage-clamp recordings were performed to isolate SK current. Results indicate that SK current amplitude (P < 0.05) and density (P < 0.01) were significantly smaller in the hypertensive group. To investigate the impact of this on intrinsic excitability, current-clamp recordings were performed in separate groups of PVN-RVLM neurons. Results indicate that the frequency of spikes evoked by current injection was significantly higher in the hypertensive group (P < 0.05-0.01). Whereas bath application of the SK channel blocker apamin significantly increased discharge of neurons from normotensive rats (P < 0.05-0.01), no effect was observed in the hypertensive group. In response to ramp current injections, subthreshold depolarizing input resistance was greater in the hypertensive group compared with the normotensive group (P < 0.05). Blockade of SK channels increased depolarizing input resistance in normotensive controls (P < 0.05) but had no effect in the hypertensive group. On termination of current pulses, a medium afterhyperpolarization potential (mAHP) was observed in most neurons of the normotensive group. In the hypertensive group, the mAHP was either small or absent. In the latter case, an afterdepolarization potential (ADP) was observed that was unaffected by apamin. Apamin treatment in the normotensive group blocked the mAHP and revealed an ADP resembling that seen in the hypertensive group. We conclude that diminished SK current likely underlies the absence of mAHPs in PVN-RVLM neurons from hypertensive rats. Both the ADP and greater depolarizing input resistance likely contribute to increased excitability of PVN-RVLM neurons from rats with AngII-Salt hypertension.

Flufenamic acid modulates multiple currents in gonadotropin-releasing hormone neurons

Reproduction in mammals is dependent upon the appropriate neurosecretion of gonadotropin-releasing hormone (GnRH), yet the endogenous generation of activity underlying GnRH secretion remains poorly understood. We have demonstrated that the depolarizing afterpotential (DAP), which modulates bursting activity, is reduced in isolated GnRH neurons from aged animals. Calcium-activated non-specific cation (CAN) channels contribute to the DAP in other vertebrate neurosecretory cells. We used the CAN channel blocker flufenamic acid (FFA) to examine the contribution of CAN channels to the DAP in GnRH neurons during aging. Recordings were performed on isolated fluorescent GnRH neurons from young, middle-aged and aged female mice. Flufenamic acid inhibited spontaneous activity, but significantly increased the DAP in neurons from young and middle-aged animals. Apamin did not significantly potentiate the DAP, but did reduce the effects of FFA, suggesting that the increased DAP is partially due to blockade of apamin-sensitive SK channels. Flufenamic acid increased the current underlying the DAP ( I ADP) and decreased the preceding fast outward current ( I OUT) at all ages. These current responses were not affected by apamin, but TEA evoked similar changes. Thus, a potassium current, likely mediated through BK channels, contributes to the fast AHP and appears to offset the DAP; this current is sensitive to FFA, but insensitive to age. The effect of FFA on the DAP, but not I ADP, is diminished in aged animals, possibly reflecting an age-related modulation of the apamin-sensitive SK channel. Future studies will examine the expression of SK channels during the aging process in GnRH neurons.

Down‐regulation of SK channel function among RVLM projecting PVN neurons (PVN‐RVLM) and sympathetic activation in AngII‐Salt hypertensive (HT) rats

A neural mechanism responsible for sympathetic activation in HT rats was investigated. We hypothesized that reduced SK current in PVN‐RVLM neurons could contribute to increased excitability and sympathoexcitation in HT rats. In voltage‐clamp recordings, the amplitude of SK current was significantly reduced in neurons from HT rats. In current‐clamp recordings, the frequency of current injection‐evoked spikes was greater in neurons from HT rats compared to normotensive (NT) controls. The SK channel blocker apamin caused a greater increase in spikes in NT controls compared to HT group. The amplitude of a medium after‐hyperpolarization potential (mAHP) was significantly reduced in the HT group. An after‐depolarization potential (ADP) was also observed in the HT group, but not in NT controls, though apamin did reveal an ADP in NT controls while failing to alter the ADP already present in the HT group. This suggests that diminished SK current likely underlies the smaller mAHP and the uncovered ADP in the HT group. Microinjection of apamin into the PVN of anesthetized rat induced a greater increase in renal SNA and MAP in NT compared to HT rats. We conclude that increased excitability of PVN‐RVLM neurons may contribute to sympathoexcitation and maintenance of AngII‐salt hypertension and reduced SK current in these neurons may constitute an underlying neural mechanism. Support: AHA0865107F (CQH) &amp; HL076312 (GMT).

Genetically Increased Cell-Intrinsic Excitability Enhances Neuronal Integration into Adult Brain Circuits

New neurons are added to the adult brain throughout life, but only half ultimately integrate into existing circuits. Sensory experience is an important regulator of the selection of new neurons but it remains unknown whether experience provides specific patterns of synaptic input or simply a minimum level of overall membrane depolarization critical for integration. To investigate this issue, we genetically modified intrinsic electrical properties of adult-generated neurons in the mammalian olfactory bulb. First, we observed that suppressing levels of cell-intrinsic neuronal activity via expression of ESKir2.1 potassium channels decreases, whereas enhancing activity via expression of NaChBac sodium channels increases survival of new neurons. Neither of these modulations affects synaptic formation. Furthermore, even when neurons are induced to fire dramatically altered patterns of action potentials, increased levels of cell-intrinsic activity completely blocks cell death triggered by NMDA receptor deletion. These findings demonstrate that overall levels of cell-intrinsic activity govern survival of new neurons and precise firing patterns are not essential for neuronal integration into existing brain circuits.

Hyped up about the hypothalamus

Hyped up about the hypothalamus

Excitability of paraventricular nucleus neurones that project to the rostral ventrolateral medulla is regulated by small‐conductance Ca2+‐activated K+ channels

Whole cell patch-clamp recordings were performed in brain slices to investigate mechanisms regulating the excitability of paraventricular nucleus (PVN) neurones that project directly to the rostral ventrolateral medulla (RVLM) (PVN-RVLM neurones) of rats. In voltage-clamp recordings, step depolarization elicited a calcium-dependent outward tail current that reversed near E(K). The current was nearly abolished by apamin and by UCL1684, suggesting mediation by small-conductance Ca(2+)-activated K(+) (SK) channels. In current-clamp recordings, depolarizing step current injections evoked action potentials that underwent spike-frequency adaptation (SFA). SK channel blockade with apamin or UCL1684 increased the spike frequency without changing the rate of SFA. Upon termination of step current injection, a prominent medium after-hyperpolarization potential (mAHP) was observed. SK channel blockade abolished the mAHP and revealed an after-depolarization potential (ADP). In response to ramp current injections, the rate of sub-threshold depolarization was increased during SK channel blockade, indicating that depolarizing input resistance was increased. Miniature EPSC frequency, amplitude, and decay kinetics were unaltered by bath application of apamin, suggesting that SK channel blockade likely increased excitability by a postsynaptic action. We conclude that although SK channels play little role in generating SFA in PVN-RVLM neurones, their activation nevertheless does dampen excitability. The mechanism appears to involve activation of a mAHP that opposes a prominent ADP that would otherwise facilitate firing.

SK Channels Gate Information Processing In Vivo by Regulating an Intrinsic Bursting Mechanism Seen In Vitro

Understanding the mechanistic substrates of neural computations that lead to behavior remains a fundamental problem in neuroscience. In particular, the contributions of intrinsic neural properties such as burst firing and dendritic morphology to the processing of behaviorally relevant sensory input have received much interest recently. Pyramidal cells within the electrosensory lateral line lobe of weakly electric fish display an intrinsic bursting mechanism that relies on somato-dendritic interactions when recorded in vitro: backpropagating somatic action potentials trigger dendritic action potentials that lead to a depolarizing afterpotential (DAP) at the soma. We recorded intracellularly from these neurons in vivo and found firing patterns that were quite different from those seen in vitro: we found no evidence for DAPs as each somatic action potential was followed by a pronounced afterhyperpolarization (AHP). Calcium chelators injected in vivo reduced the AHP, thereby unmasking the DAP and inducing in vitro-like bursting in pyramidal cells. These bursting dynamics significantly reduced the cell's ability to encode the detailed time course of sensory input. We performed additional in vivo pharmacological manipulations and mathematical modeling to show that calcium influx through N-methyl-d-aspartate (NMDA) receptors activate dendritic small conductance (SK) calcium-activated potassium channels, which causes an AHP that counteracts the DAP and leads to early termination of the burst. Our results show that ion channels located in dendrites can have a profound influence on the processing of sensory input by neurons in vivo through the modulation of an intrinsic bursting mechanism.

The role of slow potassium current in phenomena of voltage-dependent action of 4-aminopyridine in amphibian myelinated nerve fibres

The mechanism underlying the voltage-dependent action of 4-aminopyridine (4-AP) is investigated in experiments on amphibian myelinated nerve fibres (Rana ridibunda Pallas) by way of extracellular recording of electrical activity and using activators of potassium current (potassium-free solution and nitric oxide NO) and inhibitors of sodium current (tetrodotoxin). Measurement of action potential (AP) areas was used to evaluate the extent of general membrane depolarization during the activity of nerve fibres. Tetrodotoxin-induced decrease in general membrane depolarization (when the action potential amplitude was reduced by less than 20%) leads to an increase in the duration of depolarizing after-potential (DAP). This supports the dependence of time course of DAP in the presence of 4-AP on ratio of fast and slow potassium channels. In the absence of 4-AP, potassium-free solution and NO increase the potassium current through fast potassium channels (decreasing AP duration, reducing DAP and sometimes producing fast hyperpolarizing after-potential (HAP) after shortened AP), and in the presence of 4-AP these activators increase potassium current through unblocked slow potassium channels (making the development of slow HAP induced by 4-AP more rapid). The increase of slow HAP induced by 4-AP under the influence of potassium-free solution with NO supports the idea that slow HAP is due to activation of slow potassium channels and argues against the notion of removal of block of fast potassium channels. All analyzed phenomena of voltage-dependent action of 4-AP in amphibian myelinated nerve fibers can be accounted for by the activation of slow potassium current produced by membrane depolarization and a decrease of the amount of fast potassium channels involved in the membrane repolarization.

SMALL CONDUCTANCE CALCIUM‐ACTIVATED POTASSIUM CHANNELS (SK) LIMIT THE EXCITABILITY OF PVN NEURONS PROJECTING TO RVLM (PVN‐RVLM)

In vivo studies indicate that under normal condition pre‐autonomic PVN neurons are often silent or have low spontaneous activity. In spite of their importance in regulating sympathetic outflow, mechanisms that control the excitability of pre‐autonomic PVN neurons remain largely unexplored. Here, we determined the role of SK channels in limiting excitability of PVN‐RVLM neurons. In voltage‐clamp recordings, an outward current (IK) (amplitude: 72 ± 10 pA; decay constant: 234 ± 55 ms, n=8) was nearly abolished by the SK channel blocker apamin or UCL1684. Activation of IK was Ca2+ dependent and reversed at ‐97±3 mV (n=3) which was close to the EK value (‐103 mV). In current‐clamp recordings, graded current injections evoked graded increases in spike frequency. Maximum discharge was evoked by +200 pA injections and averaged 22 ± 3 Hz (n=8) and was significantly greater (P&lt;0.05) in the presence of apamin (100 nM) (47 ± 8 Hz, n=8) or UCL1684 (100 nM) (39 ± 5, n=5). Apamin and UCL1684 each blocked a prominent medium after hyperpolarization potential (mAHP: ‐11 ± 2 mV) that was evident in response to current injection. With blockade of the mAHP, a prominent after depolarization potential (ADP) was revealed (amplitude: apamin +9 ± 1; UCL1684 +7 ± 2 mV). We conclude that SK channel activation limits the excitability of PVN‐RVLM neurons. An underlying mechanism may be the ability of the mAHP to oppose the ADP. Support: AHA0865107F (QHC) &amp; HL076312 (GMT)

A self‐activating intrinsic brake on bursting in CA3 neurons

A self‐activating intrinsic brake on bursting in CA3 neurons

Wiring neurons with carbon nanotubes

GENERAL COMMENTARY article Front. Neuroeng., 29 May 2009 https://doi.org/10.3389/neuro.16.008.2009

Electrophysiological events recorded at presynaptic terminals of the crayfish neuromuscular junction with a voltage indicator

The water-soluble voltage indicator JPW1114 was used to stain thin axons and terminal varicosities of the crayfish neuromuscular junction. A slow, overnight injection protocol was developed to brightly stain fine structures without cytotoxicity. Fluorescence transients filtered at 2 kHz showed that the duration of terminal action potentials was shorter than that of those recorded in the main trunk of the axons. In addition, the repolarization phases of the terminal and axonal action potentials overlapped in time, suggesting that the entire axonal arborization repolarizes simultaneously. Manipulating resting membrane potential, +/-15-20 mV, did not alter the peak level or duration of action potentials if they fired in isolation. A prolongation of action potential, by 23%, could be induced if a 10-spike burst at 100 Hz was fired from depolarized membrane potential. No such change was observed when the high frequency train was fired from resting or hyperpolarized levels. Microelectrodes in the main trunk of axons typically recorded a depolarizing after-potential (DAP) following an action potential initiated from resting membrane potential. The DAP could be inverted and enlarged by depolarization and hyperpolarization, respectively. Fluorescence transients recorded from terminals exhibited similar DAP characteristics. The ratio of DAP to action potential amplitude recorded from terminals was similar to that recorded from the main axon. Thus, the entire axonal arborization returned to resting level in a spatially uniform manner during the DAP. The functional significance of DAP is discussed in the light of these observations.

Slack and Slick KNachannels are required for the depolarizing afterpotential of acutely isolated, medium diameter rat dorsal root ganglion neurons1

Na+-activated K+ (K(Na)) channels set and stabilize resting membrane potential in rat small dorsal root ganglion (DRG) neurons. However, whether K(Na) channels play the same role in other size DRG neurons is still elusive. The aim of this study is to identify the existence and potential physiological functions of K(Na) channels in medium diameter (25-35 microm) DRG neurons. Inside-out and whole-cell patch-clamp were used to study the electrophysiological characterizations of native K(Na) channels. RT-PCR was used to identify the existence of Slack and Slick genes. We report that K(Na) channels are required for depolarizing afterpotential (DAP) in medium sized rat DRG neurons. In inside-out patches, K(Na) channels represented 201 pS unitary chord conductance and were activated by cytoplasmic Na+ [the half maximal effective concentration (EC50): 35 mmol/L] in 160 mmol/L symmetrical K+o/K+i solution. Additionally, these K(Na) channels also represented cytoplasmic Cl(-)-dependent activation. RT-PCR confirmed the existence of Slack and Slick genes in DRG neurons. Tetrodotoxin (TTX, 100 nmol/L) completely blocked the DRG inward Na+ currents, and the following outward currents which were thought to be K(Na) currents. The DAP was increased when extracellular Na+ was replaced by Li+. We conclude that Slack and Slick K(Na) channels are required for DAP of medium diameter rat DRG neurons that regulate DRG action potential repolarization.

Regulation of somatic firing dynamics by backpropagating dendritic spikes

Pyramidal cells of the apteronotid ELL have been shown to display a characteristic mechanism of burst discharge, which has been shown to play an important role in sensory coding. This form of bursting depends on a reciprocal dendro-somatic interaction, in which discharge of a somatic spike causes a dendritic spike, which in turn contributes a dendro-somatic current flow to create a depolarizing afterpotential (DAP) in the soma. We review here our recent work showing how the timing of this DAP influences the somatic firing dynamics, and how the degree of inactivation of dendritic Na + currents can cause an increased delay between somatic and dendritic spikes. This ultimately allows the DAP to become more effective at increasing the excitability of the somatic spike generating mechanism. Further, this delay between dendritic and somatic spiking can be regulated by strongly hyperpolarizing GABA B mediated dendritic inhibition, allowing the burst dynamics to fall under synaptic regulation. In contrast, a weaker, shunting inhibition due to GABA A mediated dendritic inhibition can regulate the dendritic spike waveform to decrease the dendro-somatic current flow and the resulting DAP. We therefore show that the qualitative behaviour of an individual cell can depend on the degree of synaptic input, and the exact timing of events across the spatial extent of the neuron. Thus, our results serve to illustrate the complex dynamics that can be observed in cells with significant dendritic arborisation, a nearly ubiquitous adaptation amongst principal neurons.

Dendrites determine the contribution of after depolarization potentials (ADPs) to generation of repetitive action potentials in hypothalamic gonadotropin releasing-hormone (GnRH) neurons

The impact of structure in modulating synaptic signals originating in dendrites is widely recognized. In this study, we focused on the impact of dendrite morphology on a local spike generating mechanism which has been implicated in hormone secretion, the after depolarization potential (ADP). Using multi-compartmental models of hypothalamic GnRH neurons, we systematically truncated dendrite length and determined the consequence on ADP amplitude and repetitive firing. Decreasing the length of the dendrite significantly increased the amplitude of the ADP and increased repetitive firing. These effects were observed in dendrites both with and without active conductances suggesting they largely reflect passive characteristics of the dendrite. In order to test the findings of the model, we performed whole-cell recordings in GnRH neurons and elicited ADPs using current injection. During recordings, neurons were filled with biocytin so that we could determine dendritic and total projection (dendrite plus axon) length. Neurons exhibited ADPs and increasing ADP amplitude was associated with decreasing dendrite length, in keeping with the predictions of the models. Thus, despite the relatively simple morphology of the GnRH neuron's dendrite, it can still exert a substantial impact on the final neuronal output.

Ionic Mechanisms of Endogenous Bursting in CA3 Hippocampal Pyramidal Neurons: A Model Study

A critical property of some neurons is burst firing, which in the hippocampus plays a primary role in reliable transmission of electrical signals. However, bursting may also contribute to synchronization of electrical activity in networks of neurons, a hallmark of epilepsy. Understanding the ionic mechanisms of bursting in a single neuron, and how mutations associated with epilepsy modify these mechanisms, is an important building block for understanding the emergent network behaviors. We present a single-compartment model of a CA3 hippocampal pyramidal neuron based on recent experimental data. We then use the model to determine the roles of primary depolarizing currents in burst generation. The single compartment model incorporates accurate representations of sodium (Na+) channels (NaV1.1) and T-type calcium (Ca2+) channel subtypes (CaV3.1, CaV3.2, and CaV3.3). Our simulations predict the importance of Na+ and T-type Ca2+ channels in hippocampal pyramidal cell bursting and reveal the distinct contribution of each subtype to burst morphology. We also performed fast-slow analysis in a reduced comparable model, which shows that our model burst is generated as a result of the interaction of two slow variables, the T-type Ca2+ channel activation gate and the Ca2+-dependent potassium (K+) channel activation gate. The model reproduces a range of experimentally observed phenomena including afterdepolarizing potentials, spike widening at the end of the burst, and rebound. Finally, we use the model to simulate the effects of two epilepsy-linked mutations: R1648H in NaV1.1 and C456S in CaV3.2, both of which result in increased cellular excitability.