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Cerebellar stellate cells form inhibitory synapses with Purkinje cells, the sole output of the cerebellum. Upon stimulation by a pair of varying inhibitory and fixed excitatory presynaptic inputs, these cells do not respond to excitation (i.e., do not generate an action potential) when the magnitude of the inhibition is within a given range, but they do respond outside this range. We previously used a revised Hodgkin–Huxley type of model to study the nonmonotonic first-spike latency of these cells and their temporal increase in excitability in whole cell configuration (termed run-up). Here, we recompute these latency profiles using the same model by adapting an efficient computational technique, the two-point boundary value problem, that is combined with the continuation method. We then extend the study to investigate how switching in responsiveness, upon stimulation with presynaptic inputs, manifests itself in the context of run-up. A three-dimensional reduced model is initially derived from the original six-dimensional model and then analyzed to demonstrate that both models exhibit type 1 excitability possessing a saddle-node on an invariant cycle (SNIC) bifurcation when varying the amplitude of [Formula: see text]. Using slow-fast analysis, we show that the original model possesses three equilibria lying at the intersection of the critical manifold of the fast subsystem and the nullcline of the slow variable [Formula: see text] (the inactivation of the A-type K[Formula: see text] channel), the middle equilibrium is of saddle type with two-dimensional stable manifold (computed from the reduced model) acting as a boundary between the responsive and non-responsive regimes, and the (ghost of) SNIC is formed when the [Formula: see text]-nullcline is (nearly) tangential to the critical manifold. We also show that the slow dynamics associated with (the ghost of) the SNIC and the lower stable branch of the critical manifold are responsible for generating the nonmonotonic first-spike latency. These results thus provide important insight into the complex dynamics of stellate cells.

Loss-of-function variants in the gene SCN2A, which encodes the sodium channel NaV1.2, are strongly associated with autism spectrum disorder and intellectual disability. An estimated 20%-30% of children with these variants also suffer from epilepsy, with altered neuronal activity originating in neocortex, a region where NaV1.2 channels are expressed predominantly in excitatory pyramidal cells. This is paradoxical, as sodium channel loss in excitatory cells would be expected to dampen neocortical activity rather than promote seizure. Here, we examined pyramidal neurons lacking NaV1.2 channels and found that they were intrinsically hyperexcitable, firing high-frequency bursts of action potentials (APs) despite decrements in AP size and speed. Compartmental modeling and dynamic-clamp recordings revealed that NaV1.2 loss prevented potassium channels from properly repolarizing neurons between APs, increasing overall excitability by allowing neurons to reach threshold for subsequent APs more rapidly. This cell-intrinsic mechanism may, therefore, account for why SCN2A loss-of-function can paradoxically promote seizure.

Key points We show that NMDA receptors (NMDARs) elicit a long-term increase in the firing rates of inhibitory stellate cells of the cerebellum NMDARs induce intrinsic plasticity through a Ca2+ - and CaMKII-dependent pathway that drives shifts in the activation and inactivation properties of voltage-gated Na+ (Nav ) channels An identical Ca2+ - and CaMKII-dependent signalling pathway is triggered during whole-cell recording which lowers the action potential threshold by causing a hyperpolarizing shift in the gating properties of Nav channels. Our findings open the more general possibility that NMDAR-mediated intrinsic plasticity found in other cerebellar neurons may involve similar shifts in Nav channel gating. Abstract Memory storage in the mammalian brain is mediated not only by long-lasting changes in the efficacy of neurotransmitter receptors but also by long-term modifications to the activity of voltage-gated ion channels. Activity-dependent plasticity of voltage-gated ion channels, or intrinsic plasticity, is found throughout the brain in virtually all neuronal types, including principal cells and interneurons. Although intrinsic plasticity has been identified in neurons of the cerebellum, it has yet to be studied in inhibitory cerebellar stellate cells of the molecular layer which regulate activity outflow from the cerebellar cortex by feedforward inhibition onto Purkinje cells. The study of intrinsic plasticity in stellate cells has been particularly challenging as membrane patch breakthrough in electrophysiology experiments unintentionally triggers changes in spontaneous firing rates. Using cell-attached patch recordings to avoid disruption, we show that activation of extrasynaptic N-methyl-d-aspartate receptors (NMDARs) elicits a long-term increase in the firing properties of stellate cells by stimulating a rise in cytosolic Ca2+ and activation of Ca²⁺/calmodulin-dependent protein kinase II (CaMKII). An identical signalling pathway is triggered during whole-cell recording which lowers the action potential threshold by causing a hyperpolarizing shift in the gating properties of voltage-gated sodium (Nav ) channels. Together, our findings identify an unappreciated role of Nav channel-dependent intrinsic plasticity in cerebellar stellate cells which, in concert with non-canonical NMDAR signalling, provides the cerebellum with an unconventional mechanism to fine-tune motor behaviour.

Neuronal excitability in the vertebrate brain is governed by the coordinated activity of both ligand- and voltage-gated ion channels. In the cerebellum, spontaneous action potential (AP) firing of inhibitory stellate cells (SCs) is variable, typically operating within the 5- to 30-Hz frequency range. AP frequency is shaped by the activity of somatodendritic A-type K+channels and the inhibitory effect of GABAergic transmission. An added complication, however, is that whole-cell recording from SCs induces a time-dependent and sustained increase in membrane excitability making it difficult to define the full range of firing rates. Here, we show that whole-cell recording in cerebellar SCs of both male and female mice augments firing rates by reducing the membrane potential at which APs are initiated. AP threshold is lowered due to a hyperpolarizing shift in the gating behavior of voltage-gated Na+channels. Whole-cell recording also elicits a hyperpolarizing shift in the gating behavior of A-type K+channels which contributes to increased firing rates. Hodgkin–Huxley modeling and pharmacological experiments reveal that gating shifts in A-type K+channel activity do not impact AP threshold, but rather promote channel inactivation which removes restraint on the upper limit of firing rates. Taken together, our work reveals an unappreciated impact of voltage-gated Na+channels that work in coordination with A-type K+channels to regulate the firing frequency of cerebellar SCs.

Summary Neurotransmitter-gated ion channels are allosteric proteins that switch on and off in response to agonist binding. Most studies have focused on the agonist-bound, activated channel while assigning a lesser role to the apo or resting state. Here, we show that nanoscale mobility of resting α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA)-type ionotropic glutamate receptors (AMPA receptors) predetermines responsiveness to neurotransmitter, allosteric anions and TARP auxiliary subunits. Mobility at rest is regulated by alternative splicing of the flip/flop cassette of the ligand-binding domain, which controls motions in the distant AMPA receptor N-terminal domain (NTD). Flip variants promote moderate NTD movement, which establishes slower channel desensitization and robust regulation by anions and auxiliary subunits. In contrast, greater NTD mobility imparted by the flop cassette acts as a master switch to override allosteric regulation. In AMPA receptor heteromers, TARP stoichiometry further modifies these actions of the flip/flop cassette generating two functionally distinct classes of partially and fully TARPed receptors typical of cerebellar stellate and Purkinje cells.

Cerebellar stellate cells (CSCs) are spontaneously active, tonically firing (5-30 Hz), inhibitory interneurons that synapse onto Purkinje cells. We previously analyzed the excitability properties of CSCs, focusing on four key features: type I excitability, non-monotonic first-spike latency, switching in responsiveness and runup (i.e., temporal increase in excitability during whole-cell configuration). In this study, we extend this analysis by using whole-cell configuration to show that these neurons can also burst when treated with certain pharmacological agents separately or jointly. Indeed, treatment with 4-Aminopyridine (4-AP), a partial blocker of delayed rectifier and A-type K+ channels, at low doses induces a bursting profile in CSCs significantly different than that produced at high doses or when it is applied at low doses but with cadmium (Cd2+), a blocker of high voltage-activated (HVA) Ca2+ channels. By expanding a previously revised Hodgkin–Huxley type model, through the inclusion of Ca2+-activated K+ (K(Ca)) and HVA currents, we explain how these bursts are generated and what their underlying dynamics are. Specifically, we demonstrate that the expanded model preserves the four excitability features of CSCs, as well as captures their bursting patterns induced by 4-AP and Cd2+. Model investigation reveals that 4-AP is potentiating HVA, inducing square-wave bursting at low doses and pseudo-plateau bursting at high doses, whereas Cd2+ is potentiating K(Ca), inducing pseudo-plateau bursting when applied in combination with low doses of 4-AP. Using bifurcation analysis, we show that spike adding in square-wave bursts is non-sequential when gradually changing HVA and K(Ca) maximum conductances, delayed Hopf is responsible for generating the plateau segment within the active phase of pseudo-plateau bursts, and bursting can become “chaotic” when HVA and K(Ca) maximum conductances are made low and high, respectively. These results highlight the secondary effects of the drugs applied and suggest that CSCs have all the ingredients needed for bursting., Author summary Excitable cells, including neurons, fire action potentials (APs) in their membrane voltage that allow them to communicate with each other and to serve certain physiological purposes. They do so either tonically by firing APs periodically, or episodically by repeatedly firing clusters of APs (called bursts) separated by quiescent periods. Each one of those firing patterns can be neuron-specific and dependent on synaptic inputs and/or their physiological environment. Cerebellar stellate cells (CSCs) that synapse onto Purkinje cells, the sole output of the cerebellum responsible for motor control, are spontaneously active inhibitory interneurons that fire APs tonically. We previously studied the excitability properties of these neurons and showed that they possess several important key features, including type I excitability, runup, non-monotonic first spike latency and switching in responsiveness. In this study, we show that CSCs can also exhibit two modes of burst firing, called square-wave and pseudo-plateau, when treated with certain pharmacological agents. Using bifurcation theory, we demonstrate that spike adding in the square-wave burst is non-sequential, changing by several spikes when certain conductances are altered gradually. This study thus sheds lights onto the overall effects of the pharmacological agents and highlights the ability of CSCs to burst in certain biological conditions.

Cerebellar stellate cells are inhibitory molecular interneurons that regulate the firing properties of Purkinje cells, the sole output of cerebellar cortex. Recent evidence suggests that these cells exhibit temporal increase in excitability during whole-cell patch-clamp configuration in a phenomenon termed runup. They also exhibit a non-monotonic first-spike latency profile as a function of the holding potential in response to a fixed step-current. In this study, we use modeling approaches to unravel the dynamics of runup and categorize the firing behavior of cerebellar stellate cells as either type I or type II oscillators. We then extend this analysis to investigate how the non-monotonic latency profile manifests itself during runup. We employ a previously developed, but revised, Hodgkin–Huxley type model to show that stellate cells are indeed type I oscillators possessing a saddle node on an invariant cycle (SNIC) bifurcation. The SNIC in the model acts as a “threshold” for tonic firing and produces a slow region in the phase space called the ghost of the SNIC. The model reveals that (i) the SNIC gets left-shifted during runup with respect to I app = I test in the current-step protocol, and (ii) both the distance from the stable limit cycle along with the slow region produce the non-monotonic latency profile as a function of holding potential. Using the model, we elucidate how latency can be made arbitrarily large for a specific range of holding potentials close to the SNIC during pre-runup (post-runup). We also demonstrate that the model can produce transient single spikes in response to step-currents entirely below ISNIC, and that a pair of dynamic inhibitory and excitatory post-synaptic inputs can robustly evoke action potentials, provided that the magnitude of the inhibition is either low or high but not intermediate. Our results show that the topology of the SNIC is the key to explaining such behaviors.