Theoretical investigation of the neuronal Na+ channel SCN1A: abnormal gating and epilepsy

The Hodgkin-Huxley-Katz Prize Lecture: A Markov model with permeation-dependent gating that accounts for resurgent current of voltage-gated Na channels

Many neurons that fire high-frequency action potentials express specialized voltage-gated Na channel complexes that not only conduct transient current upon depolarization, but also pass resurgent current upon repolarization. The resurgent current is associated with recovery of transient current, even at moderately negative potentials where fast inactivation is usually absorbing. The combined results of many experimental studies have led to the hypothesis that resurgent current flows upon repolarization when an endogenous blocking protein that occludes open channels at depolarized potentials is expelled by inwardly permeating Na ions. Additional observations have suggested that the position of the voltage sensor of domain IV regulates the affinity of the channel for the putative blocker. To test the effectiveness of a kinetic scheme incorporating these features, here we develop and justify a Markov model with states grounded in known Na channel conformations. Simulations were designed to investigate whether including a permeation-dependent unblocking rate constant and two open-blocked states, superimposed on conformations and voltage-sensitive movements present in all voltage-gated Na channels, is sufficient to account for the unusual gating of channels with a resurgent component. Optimizing rate constant parameters against a wide range of experimental data from cerebellar Purkinje cells demonstrates that a kinetic scheme for Na channels incorporating the novel aspects of a permeation-dependent unblock, as well as distinct high- and low-affinity blocked states, reproduces all the attributes of experimentally recorded Na currents in a physiologically plausible manner.

Bayesian inference for biophysical neuron models enables stimulus optimization for retinal neuroprosthetics

While multicompartment models have long been used to study the biophysics of neurons, it is still challenging to infer the parameters of such models from data including uncertainty estimates. Here, we performed Bayesian inference for the parameters of detailed neuron models of a photoreceptor and an OFF- and an ON-cone bipolar cell from the mouse retina based on two-photon imaging data. We obtained multivariate posterior distributions specifying plausible parameter ranges consistent with the data and allowing to identify parameters poorly constrained by the data. To demonstrate the potential of such mechanistic data-driven neuron models, we created a simulation environment for external electrical stimulation of the retina and optimized stimulus waveforms to target OFF- and ON-cone bipolar cells, a current major problem of retinal neuroprosthetics.

Na+ microdomains and sparks: Role in cardiac excitation-contraction coupling and arrhythmias in ankyrin-B deficiency

Cardiac sodium (Na⁺) potassium ATPase (NaK) pumps, neuronal sodium channels (I_Na), and sodium calcium (Ca²⁺) exchangers (NCX1) may co-localize to form a Na⁺ microdomain. It remains controversial as to whether neuronal I_Na contributes to local Na⁺ accumulation, resulting in reversal of nearby NCX1 and influx of Ca²⁺ into the cell. Therefore, there has been great interest in the possible roles of a Na⁺ microdomain in cardiac Ca²⁺-induced Ca²⁺ release (CICR). In addition, the important role of co-localization of NaK and NCX1 in regulating localized Na⁺ and Ca²⁺ levels and CICR in ankyrin-B deficient (ankyrin-B^+/-) cardiomyocytes has been examined in many recent studies. Altered Na⁺ dynamics may contribute to the appearance of arrhythmias, but the mechanisms underlying this relationship remain unclear. In order to investigate this, we present a mechanistic canine cardiomyocyte model which reproduces independent local dyadic junctional SR (JSR) Ca²⁺ release events underlying cell-wide excitation-contraction coupling, as well as a three-dimensional super-resolution model of the Ca²⁺ spark that describes local Na⁺ dynamics as governed by NaK pumps, neuronal I_Na, and NCX1. The model predicts the existence of Na⁺ sparks, which are generated by NCX1 and exhibit significantly slower dynamics as compared to Ca²⁺ sparks. Moreover, whole-cell simulations indicate that neuronal I_Na in the cardiac dyad plays a key role during the systolic phase. Rapid inward neuronal I_Na can elevate dyadic [Na⁺] to 35-40 mM, which drives reverse-mode NCX1 transport, and therefore promotes Ca²⁺ entry into the dyad, enhancing the trigger for JSR Ca²⁺ release. The specific role of decreased co-localization of NaK and NCX1 in ankyrin-B^+/- cardiomyocytes was examined. Model results demonstrate that a reduction in the local NCX1- and NaK-mediated regulation of dyadic [Ca²⁺] and [Na⁺] results in an increase in Ca²⁺ spark activity during isoproterenol stimulation, which in turn stochastically activates NCX1 in the dyad. This alteration in NCX1/NaK co-localization interrupts the balance between NCX1 and NaK currents in a way that leads to enhanced depolarizing inward current during the action potential plateau, which ultimately leads to a higher probability of L-type Ca²⁺ channel reopening and arrhythmogenic early-afterdepolarizations.

Dynamical characterization of inactivation path in voltage-gated Na(+) ion channel by non-equilibrium response spectroscopy

Inactivation path of voltage gated sodium channel has been studied here under various voltage protocols as it is the main governing factor for the periodic occurrence and shape of the action potential. These voltage protocols actually serve as non-equilibrium response spectroscopic tools to study the ion channel in non-equilibrium environment. In contrast to a lot of effort in finding the crystal structure based molecular mechanism of closed-state(CSI) and open-state inactivation(OSI); here our approach is to understand the dynamical characterization of inactivation. The kinetic flux as well as energetic contribution of the closed and open- state inactivation path is compared here for voltage protocols, namely constant, pulsed and oscillating. The non-equilibrium thermodynamic quantities used in response to these voltage protocols serve as improved characterization tools for theoretical understanding which not only agrees with the previously known kinetic measurements but also predict the energetically optimum processes to sustain the auto-regulatory mechanism of action potential and the consequent inactivation steps needed. The time dependent voltage pattern governs the population of the conformational states which when couple with characteristic rate parameters, the CSI and OSI selectivity arise dynamically to control the inactivation path. Using constant, pulsed and continuous oscillating voltage protocols we have shown that during depolarization the OSI path is more favored path of inactivation however, in the hyper-polarized situation the CSI is favored. It is also shown that the re-factorisation of inactivated sodium channel to resting state occurs via CSI path. Here we have shown how the subtle energetic and entropic cost due to the change in the depolarization magnitude determines the optimum path of inactivation. It is shown that an efficient CSI and OSI dynamical profile in principle can characterize the open-state drug blocking phenomena.

NaV1.1 channels in axon initial segments of bipolar cells augment input to magnocellular visual pathways in the primate retina

In the primate visual system, the ganglion cells of the magnocellular pathway underlie motion and flicker detection and are relatively transient, while the more sustained ganglion cells of the parvocellular pathway have comparatively lower temporal resolution, but encode higher spatial frequencies. Although it is presumed that functional differences in bipolar cells contribute to the tuning of the two pathways, the properties of the relevant bipolar cells have not yet been examined in detail. Here, by making patch-clamp recordings in acute slices of macaque retina, we show that the bipolar cells within the magnocellular pathway, but not the parvocellular pathway, exhibit voltage-gated sodium (NaV), T-type calcium (CaV), and hyperpolarization-activated, cyclic nucleotide-gated (HCN) currents, and can generate action potentials. Using immunohistochemistry in macaque and human retinae, we show that NaV1.1 is concentrated in an axon initial segment (AIS)-like region of magnocellular pathway bipolar cells, a specialization not seen in transient bipolar cells of other vertebrates. In contrast, CaV3.1 channels were localized to the somatodendritic compartment and proximal axon, but were excluded from the AIS, while HCN1 channels were concentrated in the axon terminal boutons. Simulations using a compartmental model reproduced physiological results and indicate that magnocellular pathway bipolar cells initiate spikes in the AIS. Finally, we demonstrate that NaV channels in bipolar cells augment excitatory input to parasol ganglion cells of the magnocellular pathway. Overall, the results demonstrate that selective expression of voltage-gated channels contributes to the establishment of parallel processing in the major visual pathways of the primate retina.

Kinetic model of Nav1.5 channel provides a subtle insight into slow inactivation associated excitability in cardiac cells

Voltage-gated sodium channel Nav1.5 has been linked to the cardiac cell excitability and a variety of arrhythmic syndromes including long QT, Brugada, and conduction abnormalities. Nav1.5 exhibits a slow inactivation, corresponding to a duration-dependent bi-exponential recovery, which is often associated with various arrhythmia syndromes. However, the gating mechanism of Nav1.5 and the physiological role of slow inactivation in cardiac cells remain elusive. Here a 12-state two-step inactivation Markov model was successfully developed to depict the gating kinetics of Nav1.5. This model can simulate the Nav1.5 channel in not only steady state processes, but also various transient processes. Compared with the simpler 8-state model, this 12-state model is well-behaved in simulating and explaining the processes of slow inactivation and slow recovery. This model provides a good framework for further studying the gating mechanism and physiological role of sodium channel in excitable cells.

Kinetic modeling of Nav1.7 provides insight into erythromelalgia-associated F1449V mutation

Gain-of-function mutations of the voltage-gated sodium channel (VGSC) Na(v)1.7 have been linked to human pain disorders. The mutation F1449V, located at the intracellular end of transmembrane helix S6 of domain III, induces the inherited pain syndrome erythromelalgia. A kinetic model of wild-type (WT) and F1449V Na(v)1.7 may provide a basis for predicting putative intraprotein interactions. We semiautomatically constrained a Markov model using stochastic search algorithms and whole cell patch-clamp recordings from human embryonic kidney cells transfected with Na(v)1.7 and its F1449V mutation. The best models obtained simulated known differences in action potential thresholds and firing patterns in spinal sensory neurons expressing WT and F1449V. The most suitable Markov model consisted of three closed, one open, and two inactivated states. The model predicted that the F1449V mutation shifts occupancy of the closed states closer to the open state, making it easier for the channel pore to open. It also predicted that F1449V's second inactivated state is more than four times more likely to be occupied than the equivalent state in WT at hyperpolarized potentials, although the mutation still lowered the firing threshold of action potentials. The differences between WT and F1449V were not limited to a single transition. Thus a point mutation in position F1449, while phenotypically most probably affecting the activation gate, may also modify channel functions mediated by structures in more distant areas of the channel protein.

A computational model of Purkinje fibre single cell electrophysiology: implications for the long QT syndrome

Computer modelling has emerged as a particularly useful tool in understanding the physiology and pathophysiology of cardiac tissues. Models of ventricular, atrial and nodal tissue have evolved and include detailed ion channel kinetics and intercellular Ca(2+) handling. Purkinje fibre cells play a central role in the electrophysiology of the heart and in the genesis of cardiac arrhythmias. In this study, a new computational model has been constructed that incorporates the major membrane currents that have been isolated in recent experiments using Purkinje fibre cells. The model, which integrates mathematical models of human ion channels based on detailed biophysical studies of their kinetic and voltage-dependent properties, recapitulates distinct electrophysiological characteristics unique to Purkinje fibre cells compared to neighbouring ventricular myocytes. These characteristics include automaticity, hyperpolarized voltage range of the action potential plateau potential, and prolonged action potential duration. Simulations of selective ion channel blockade reproduce responses to pharmacological challenges characteristic of isolated Purkinje fibres in vitro, and importantly, the model predicts that Purkinje fibre cells are prone to severe arrhythmogenic activity in patients harbouring long QT syndrome 3 but much less so for other common forms of long QT. This new Purkinje cellular model can be a useful tool to study tissue-specific drug interactions and the effects of disease-related ion channel dysfunction on the cardiac conduction system.

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 (Na_V1.1) and T-type calcium (Ca²⁺) channel subtypes (Ca_V3.1, Ca_V3.2, and Ca_V3.3). 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 Na_V1.1 and C456S in Ca_V3.2, both of which result in increased cellular excitability.

Excitation Control: Balancing PSD-95 Function at the Synapse

Excitability of individual neurons dictates the overall excitation in specific brain circuits. This process is thought to be regulated by molecules that regulate synapse number, morphology and strength. Neuronal excitation is also influenced by the amounts of neurotransmitter receptors and signaling molecules retained at particular synaptic sites. Recent studies revealed a key role for PSD-95, a scaffolding molecule enriched at glutamatergic synapses, in modulation of clustering of several neurotransmitter receptors, adhesion molecules, ion channels, cytoskeletal elements and signaling molecules at postsynaptic sites. In this review we will highlight mechanisms that control targeting of PSD-95 at the synapse, and discuss how this molecule influences the retention and clustering of diverse synaptic proteins to regulate synaptic structure and strength. We will also discuss how PSD-95 may maintain a balance between excitation and inhibition in the brain and how alterations in this balance may contribute to neuropsychiatric disorders.

Excitation Control: Balancing PSD-95 Function at the Synapse

Excitability of individual neurons dictates the overall excitation in specific brain circuits. This process is thought to be regulated by molecules that regulate synapse number, morphology and strength. Neuronal excitation is also influenced by the amounts of neurotransmitter receptors and signaling molecules retained at particular synaptic sites. Recent studies revealed a key role for PSD-95, a scaffolding molecule enriched at glutamatergic synapses, in modulation of clustering of several neurotransmitter receptors, adhesion molecules, ion channels, cytoskeletal elements and signaling molecules at postsynaptic sites. In this review we will highlight mechanisms that control targeting of PSD-95 at the synapse, and discuss how this molecule influences the retention and clustering of diverse synaptic proteins to regulate synaptic structure and strength. We will also discuss how PSD-95 may maintain a balance between excitation and inhibition in the brain and how alterations in this balance may contribute to neuropsychiatric disorders.

Periodicity in Na+ channel properties alters excitability of a model neuron

The voltage gated Na channels play vital role in action potential waveform shaping and propagation. We have shown earlier that the duration and amplitude of a prolonged depolarization alter all the steady state and kinetic parameters of rNa(v)1.2a voltage gated Na channel in a pseudo-oscillatory fashion. In the present study, we show that the Hodgkin-Huxley voltage and time dependent rate constants of activation (alpha(m) and beta(m)) and fast inactivation (alpha(h) and beta(h)), obtained from the analyses of Na currents and steady state activation and inactivation plots, following application of prepulses in both slow (1-100s) and fast (100-1000ms) ranges, vary with the duration of a prepulse in a pseudo-oscillatory manner. Using these Hodgkin-Huxley kinetic parameters in simulation, the excitability and firing pattern of a model neuron are shown to vary in a history dependent periodic fashion.

Computational analysis of the R85C and R85H epilepsy mutations in Na+ channel β1 subunits

Mutations in Na+ channels cause a variety of epilepsy syndromes. Analysis of these mutations shows a range of simultaneous functional consequences, each of which may increase or decrease membrane excitability, making it difficult to predict the combined effect on neuron firing. This may be addressed by building mathematical models of Na+ channel gating and using them in neuron models to predict responses to natural stimuli. The R85C and R85H mutations of the beta1 subunit cause generalized epilepsy syndromes in humans, and an experimental study showed that these mutations shift steady-state activation in the negative direction, which predicts increased excitability, and shift fast inactivation in the negative direction, which predicts decreased excitability. In addition, the R85C also shifts slow inactivation in the negative direction. To predict changes in neuron excitability resulting from these contradictory effects we built Na+ channel models based on our earlier data and on new measurements of the rate of slow inactivation over a range of potentials. Use of these Na+ channel models in simple neuron models revealed that both mutations cause an increase in excitability but the R85H mutation was more excitable. This is due to differences in steady-state slow inactivation and to subtle differences in fast kinetics captured by the model fitting process. To understand the effect of changes in different gating processes and to provide a simple guide for interpreting changes caused by mutations, we performed a sensitivity analysis. Using the wild-type model we shifted each activation curve by +/-5 mV or altered gating rates up or down by 20%. Excitability was most sensitive to changes in voltage dependence of activation, followed by voltage dependence of inactivation and then slow inactivation. By contrast, excitability was relatively insensitive to gating rates.

Impaired inactivation gate stabilization predicts increased persistent current for an epilepsy-associated SCN1A mutation

Mutations in SCN1A (encoding the neuronal voltage-gated sodium channel alpha1 subunit, Na(V)1.1, or SCN1A) are associated with genetic epilepsy syndromes including generalized epilepsy with febrile seizures plus (GEFS+) and severe myoclonic epilepsy of infancy. Here, we present the formulation and use of a computational model for SCN1A to elucidate molecular mechanisms underlying the increased persistent sodium current exhibited by the GEFS+ mutant R1648H. Our model accurately reproduces all experimentally measured SCN1A whole-cell biophysical properties including biphasic whole-cell current decay, channel activation, and entry into and recovery from fast and slow inactivation. The model predicts that SCN1A open-state inactivation results from a two-step process that can be conceptualized as initial gate closure, followed by recruitment of a mechanism ("latch") to stabilize the inactivated state. Selective impairment of the second latching step results in an increase in whole-cell persistent current similar to that observed for the GEFS+ mutant R1648H. These results provide a deeper level of understanding of mutant SCN1A dysfunction in an inherited epilepsy syndrome, which will enable more precise computational studies of abnormal neuronal activity in epilepsy and may help guide new targeted therapeutic strategies.

Single-channel properties of human NaV1.1 and mechanism of channel dysfunction in SCN1A-associated epilepsy

Mutations in genes encoding neuronal voltage-gated sodium channel subunits have been linked to inherited forms of epilepsy. The majority of mutations (>100) associated with generalized epilepsy with febrile seizures plus (GEFS+) and severe myoclonic epilepsy of infancy (SMEI) occur in SCN1A encoding the Na_V1.1 neuronal sodium channel α-subunit. Previous studies demonstrated functional heterogeneity among mutant SCN1A channels, revealing a complex relationship between clinical and biophysical phenotypes. To further understand the mechanisms responsible for mutant SCN1A behavior, we performed a comprehensive analysis of the single-channel properties of heterologously expressed recombinant WT-SCN1A channels. Based on these data, we then determined the mechanisms for dysfunction of two GEFS+-associated mutations (R1648H, R1657C) both affecting the S4 segment of domain 4. WT-SCN1A has a slope conductance (17 pS) similar to channels found in native mammalian neurons. The mean open time is ∼0.3 ms in the −30 to −10 mV range. The R1648H mutant, previously shown to display persistent sodium current in whole-cell recordings, exhibited similar slope conductance but had an increased probability of late reopening and a subfraction of channels with prolonged open times. We did not observe bursting behavior and found no evidence for a gating mode shift to explain the increased persistent current caused by R1648H. Cells expressing R1657C exhibited conductance, open probability, mean open time, and latency to first opening similar to WT channels but reduced whole-cell current density, suggesting decreased number of functional channels at the plasma membrane. In summary, our findings define single-channel properties for WT-SCN1A, detail the functional phenotypes for two human epilepsy-associated sodium channel mutants, and clarify the mechanism for increased persistent sodium current induced by the R1648H allele.

Involvement of Scn1b and Kcna1 ion channels in audiogenic seizures and PTZ-induced epilepsy

We have undertaken chemical genetic approach using Qingyangshenylycosides (QYS), a natural product compound, to explore the molecular mechanisms underlying different types of epilepsy models. Two animal models were used for these studies, i.e., audiogenic seizure (AGS) and pentylenetetrazol (PTZ)-induced generalized epilepsy in DBA/2J mice. We show that the latency of AGS is prolonged and the severity of seizures (the percentages of the tonus, Tonus_%) is reduced in the QYS-treated animals. These results indicate that QYS has anticonvulsant effect on the AGS model. However, we find that administration of QYS has an opposite effects on PTZ-induced generalized epilepsy. Both the latency of the generalized epilepsy and the latency of death are decreased after QYS treatment in PTZ-induced epilepsy. We examine the molecular basis of the distinct roles of QYS in these two epilepsy models by using gene expression data. Our results show that a voltage-gated sodium channel (Scn1b) and a voltage-gated potassium channel (Kcna1) are differentially expressed in AGS and PTZ-induced epilepsy models as well as in QYS-treated animals. Our results demonstrate that a chemical genetic approach may help to reveal both the molecular mechanisms of different epilepsies and the mechanism of action of the antiepileptic drugs.

Calmodulin Mediates Ca2+ Sensitivity of Sodium Channels

Ca2+ has been proposed to regulate Na+ channels through the action of calmodulin (CaM) bound to an IQ motif or through direct binding to a paired EF hand motif in the Nav1 C terminus. Mutations within these sites cause cardiac arrhythmias or autism, but details about how Ca2+ confers sensitivity are poorly understood. Studies on the homologous Cav1.2 channel revealed non-canonical CaM interactions, providing a framework for exploring Na+ channels. In contrast to previous reports, we found that Ca2+ does not bind directly to Na+ channel C termini. Rather, Ca2+ sensitivity appears to be mediated by CaM bound to the C termini in a manner that differs significantly from CaM regulation of Cav1.2. In Nav1.2 or Nav1.5, CaM bound to a localized region containing the IQ motif and did not support the large Ca(2+)-dependent conformational change seen in the Cav1.2.CaM complex. Furthermore, CaM binding to Nav1 C termini lowered Ca2+ binding affinity and cooperativity among the CaM-binding sites compared with CaM alone. Nonetheless, we found suggestive evidence for Ca2+/CaM-dependent effects upon Nav1 channels. The R1902C autism mutation conferred a Ca(2+)-dependent conformational change in Nav1.2 C terminus.CaM complex that was absent in the wild-type complex. In Nav1.5, CaM modulates the Cterminal interaction with the III-IV linker, which has been suggested as necessary to stabilize the inactivation gate, to minimize sustained channel activity during depolarization, and to prevent cardiac arrhythmias that lead to sudden death. Together, these data offer new biochemical evidence for Ca2+/CaM modulation of Na+ channel function.