Abstract Pacemaking neurons, often found in mammalian nervous systems, integrate their inputs differently than quiescent neurons. Rhythmic single-spike pacemaking that is robust to noise can be achieved with a slow process that enforces a “resting potential” at each point along a ramp-like interspike interval (ISI) coupled with a fast restorative component. To demonstrate this phenomenon, we modeled previously identified distinct subpopulations of midbrain dopamine neurons that differed in projection target and in the regularity of their pacemaking. In the model of the more regularly-firing subpopulation projecting to the dorsomedial striatum, K V 4 current was recruited by a deep after-hyperpolarizing potential (AHP) mediated by the SK channel. In the model of the less regularly-firing subpopulation projecting to the medial shell of the nucleus accumbens, the AHP was too shallow to recruit the K V 4 current. In the more regularly firing population, the trajectory in the phase space of membrane potential and slow inactivation of K V 4 was confined to move slowly through a narrow channel during the ramp-like portion of the ISI. Noisy perturbations from this channel were quickly damped by fast activation of K V 4. In contrast, the smaller AHP in the model of the subpopulation projecting to the medial shell of the nucleus accumbens failed to recruit Kv4-mediated current, therefore the narrow channel was never entered, greatly decreasing the regularity in the presence of noise. This mechanism may be broadly applicable to single-spike pacemakers and explains how slow pacemaking with small net currents can be robust to fluctuations in single channel openings. Author Summary Pacemaking cells spike at regular intervals without the need for external input. There are numerous examples of pacemaking cells in the nervous system. We show that a process with slow dynamics relative to the individual spikes can make regular pacemaking robust to the noise that is always present in biological systems.

Gamma oscillations (40-140 Hz) play a fundamental role in neural coordination and cognitive functions in the medial entorhinal cortex (mEC). While previous studies suggest that pyramidal-interneuron network gamma (PING) and interneuron network gamma (ING) mechanisms contribute to these oscillations, the precise role of inhibitory circuits remains unclear. Using optogenetic stimulation and whole-cell electrophysiology in acute mouse brain slices, we examined synaptic input and spike timing in neurons across layer II/III mEC. We found that fast-spiking interneurons exhibited robust gamma-frequency firing, while excitatory neurons engaged in gamma cycle skipping. Stellate and pyramidal cells received minimal recurrent excitation, whereas fast-spiking interneurons received strong excitatory input. Both excitatory neurons and fast-spiking interneurons received gamma-frequency inhibition, emphasizing the role of recurrent inhibition in gamma rhythms. Gamma activity was reduced but persisted after AMPA/kainate receptor blockade, indicating that interneurons can sustain oscillations via an ING mechanism. Selective activation of PV+ interneurons confirmed their ability to sustain fast gamma inhibition autonomously. To further assess the interplay of excitation and inhibition, we developed computational network models constrained by our experimental data. Simulations revealed that weak excitatory input to interneurons supports fast ING-dominated rhythms (∼100-140 Hz) while strengthening excitatory drive induces a transition to slower PING-dominated oscillations (60-100 Hz), although this regime shift was not observed consistently after AMPA/kainate receptor block. These findings highlight the dominant role of inhibitory circuits in sustaining gamma rhythms, demonstrate how excitation strength tunes the oscillatory regime, and refine models of entorhinal gamma oscillations critical for spatial memory processing.

Theta-nested gamma oscillations in the medial entorhinal cortex (mEC) are essential for spatial coding and memory, but the underlying cellular mechanisms remain unclear. We combined optogenetics, whole-cell electrophysiology, intracellular voltage imaging, and local field potential (LFP) recordings in acute slices from CaMKIIα-ChR2 mice to investigate how excitation and inhibition shape theta-gamma coupling in layer II/III mEC. During theta-frequency stimulation, fast-spiking interneurons received strong gamma-frequency excitation and fired rhythmic bursts, whereas stellate and pyramidal neurons fired more sparsely and were dominated by gamma-frequency inhibition. This sparse firing could support the selective firing of grid cells. Excitatory post-synaptic currents in interneurons preceded inhibitory currents and LFP gamma by ~3 ms, supporting a pyramidal-interneuron network gamma (PING) mechanism. Pyramidal neurons fired on the descending phase of the gamma cycle, whereas stellate cells and fast-spiking interneurons fired before and after the trough, respectively. Intracellular voltage imaging revealed network gamma synchronization among excitatory neurons at a population level, with topographic clustering of subthreshold membrane potentials, but not spike timing, while individual neurons often skipped gamma cycles. These findings identify the dominant role of reciprocal E-I interactions in generating theta-nested gamma oscillations and highlight distinct cell-type contributions to the temporal dynamics of the mEC. Further, a biophysically realistic computational model predicted gamma cycle skipping in stellate cells and burst firing in fast-spiking interneurons during PING. Our experimental and computational results provide mechanistic insight into how the intrinsic properties of mEC cell types generate oscillatory activity in a manner that could support grid cell function and spatial computation.

Dopamine neurons projecting to distinct brain regions have unique biophysical properties, which are thought to reflect functional specialization. One of these defining properties is the duration of hyperpolarization-induced firing pauses, or rebound delays, which are longer in atypical dopamine neurons targeting ventromedial striatal areas like the nucleus accumbens core. Differences in rebound delay are determined by Kv4 channel-mediated A-type currents, but the mechanisms underlying these differences and their functional implications are not well understood. We hypothesized that KChIP4a, a unique Kv4 β-subunit splice variant, determines rebound delay duration in atypical dopamine neurons. To test this, we generated a transgenic mouse line with dopamine neuron-selective removal of KChIP4a. We found that KChIP4a deletion shortened rebound delays in core-projecting atypical dopamine neurons by changing A-type current kinetics, without affecting conventional dopamine neurons. This indicates that KChIP4a acts as a selective biophysical amplifier of hyperpolarizing inhibition in core-projecting dopamine neurons, and computational modeling suggests that this effect is robust across a wide range of in vivo-like conditions for excitation/inhibition balance. Since firing pauses in core-projecting dopamine neurons are thought to drive learning from reward omission, or negative prediction errors, we tested the effect of KChIP4a deletion on different types of behavior in male and female mice. We found that removal of KChIP4a from dopamine neurons selectively accelerated learning from negative prediction errors, without affecting learning from positive prediction errors or other behavioral variables. Together, our results suggest that KChIP4a fine-tunes subthreshold excitability in projection-defined dopamine neuron populations to regulate specific types of learning.

Dopamine (DA) midbrain neurons are involved in a wide array of key brain functions including movement control and reward-based learning. They are also critical for major brain disorders such as Parkinson's disease or schizophrenia. DA neurons projecting to distinct striatal territories are diverse with regard to their molecular makeup and cellular physiology, which are likely to contribute to the observed differences in temporal DA dynamics. Among these regions, the dorsolateral striatum (DLS) displays the fastest DA dynamics, which might control the moment-to-moment vigor and variability of voluntary movements. However, the underlying mechanisms for these DLS-specific fast DA fluctuations are unresolved. Here, we show that DLS-projecting DA neurons in the substantia nigra (SN) possess a unique biophysical profile allowing immediate 10-fold accelerations in discharge frequency via rebound bursting. By using a combination of in vitro patch-clamp recordings in projection-defined DA SN subpopulations from adult male mice and developing matching projection-specific computational models, we demonstrate that a strong interaction of Cav3 and SK channels specific for DLS-projecting Aldh1a1-positive DA SN (DLS-DA) neurons controls the gain of fast rebound bursting, while Kv4 and HCN channels mediate timing of rebound excitability. In addition, GIRK channels activated by D2 and GABAB receptors prevent rebound bursting in these DLS-DA neurons. Furthermore, our in vivo patch-clamp recordings and matching in vivo computational models provide evidence that these unique rebound properties might be preserved in the intact brain, where they might endow specific computational properties well suited for the generation of fast DA dynamics present in DLS.

A mean field method for pulse-coupled oscillators with delays used a self-connected oscillator to represent a synchronous cluster of N - 1 oscillators and a single oscillator assumed to be perturbed from the cluster. A periodic train of biexponential conductance input was divided into a tonic and a phasic component representing the mean field input. A single cycle of the phasic conductance from the cluster was applied to the single oscillator embedded in the tonic component at different phases to measure the change in the cycle length in which the perturbation was initiated, that is, the first-order phase response curve (PRC), and the second-order PRC in the following cycle. A homogeneous network of 100 biophysically calibrated inhibitory interneurons with either shunting or hyperpolarizing inhibition tested the predictive power of the method. A self-consistency criterion predicted the oscillation frequency of the network from the PRCs as a function of the synaptic delay. The major determinant of the stability of synchrony was the sign of the slope of the first-order PRC of the single oscillator in response to an input from the self-connected cluster at a phase corresponding to the delay value. For most short delays, first-order PRCs correctly predicted the frequency and stability of simulated network activity. However, considering the second-order PRC improved the frequency prediction and resolved an incorrect prediction of stability of global synchrony at delays close to the free running period of single neurons in which a discontinuity in the PRC precluded existence of 1:1 self-locking.NEW & NOTEWORTHY A mean field theory for synchrony in neural networks in which neurons are generally above threshold in the mean-driven regime is developed to extend and complement mean field theory previously developed by others for neurons that are generally below threshold in the fluctuation-driven regime. This work extends phase response curve theory as applied to high-frequency oscillations in networks with synaptic inputs that are not short with respect to the network period.

Persistent activity in excitatory pyramidal cells (PYRs) is a putative mechanism for maintaining memory traces during working memory. We have recently demonstrated persistent interruption of firing in fast-spiking parvalbumin-expressing interneurons (PV-INs), a phenomenon that could serve as a substrate for persistent activity in PYRs through disinhibition lasting hundreds of milliseconds. Here, we find that hippocampal CA1 PV-INs exhibit type 2 excitability, like striatal and neocortical PV-INs. Modeling and mathematical analysis showed that the slowly inactivating potassium current KV1 contributes to type 2 excitability, enables the multiple firing regimes observed experimentally in PV-INs, and provides a mechanism for robust persistent interruption of firing. Using a fast/slow separation of times scales approach with the KV1 inactivation variable as a bifurcation parameter shows that the initial inhibitory stimulus stops repetitive firing by moving the membrane potential trajectory onto a coexisting stable fixed point corresponding to a nonspiking quiescent state. As KV1 inactivation decays, the trajectory follows the branch of stable fixed points until it crosses a subcritical Hopf bifurcation (HB) and then spirals out into repetitive firing. In a model describing entorhinal cortical PV-INs without KV1, interruption of firing could be achieved by taking advantage of the bistability inherent in type 2 excitability based on a subcritical HB, but the interruption was not robust to noise. Persistent interruption of firing is therefore broadly applicable to PV-INs in different brain regions but is only made robust to noise in the presence of a slow variable, KV1 inactivation.

Synchronization in the gamma band (25-150 Hz) is mediated by PV+ inhibitory interneurons, and evidence is accumulating for the essential role of gamma oscillations in cognition. Oscillations can arise in inhibitory networks via synaptic interactions between individual oscillatory neurons (mean -driven) or via strong recurrent inhibition that destabilizes the stationary background firing rate in the fluctuationdriven balanced state, causing an oscillation in the population firing rate. Previous theoretical work focused on model neurons with Hodgkin's Type 1 excitability (integrators) connected by current -based synapses. Here we show that networks comprised of simple Type 2 oscillators (resonators) exhibit a supercritical Hopf bifurcation between synchrony and asynchrony and a gradual transition via cycle skipping from coupled oscillators to stochastic population oscillator (SPO), as previously shown for Type 1. We extended our analysis to homogeneous networks with conductance rather than current based synapses and found that networks with hyperpolarizing inhibitory synapses were more robust to noise than those with shunting synapses, both in the coupled oscillator and SPO regime. Assuming that reversal potentials are uniformly distributed between shunting and hyperpolarized values, as observed in one experimental study, converting synapses to purely hyperpolarizing favored synchrony in all cases, whereas conversion to purely shunting synapses made synchrony less robust except at very high conductance strengths. In mature neurons the synaptic reversal potential is controlled by chloride cotransporters that control the intracellular concentrations of chloride and bicarbonate ions, suggesting these transporters as a potential therapeutic target to enhance gamma synchrony and cognition.

Phase Response Curves (PRCs) have been useful in determining and analyzing various phase-locking modes in networks of oscillators under pulse-coupling assumptions, as reviewed in Mathematical Biosciences, 226:77-96, 2010. Here, we update that review to include progress since 2010 on pulse coupled oscillators with conduction delays. We then present original results that extend the derivation of the criteria for stability of global synchrony in networks of pulse-coupled oscillators to include conduction delays. We also incorporate conduction delays to extend previous studies that showed how an alternating firing pattern between two synchronized clusters could enforce within cluster synchrony, even for clusters unable to synchronize themselves in isolation. To obtain these results, we used self-connected neurons to represent clusters. These results greatly extend the applicability of the stability analyses to networks of pulse-coupled oscillators since conduction delays are ubiquitous and strongly impact the stability of synchrony. Although these analyses only strictly apply to identical oscillators with identical connections to other oscillators, the principles are general and suggest how to promote or impede synchrony in physiological networks of neurons, for example. Heterogeneity can be interpreted as a form of frozen noise, and approximate synchrony can be sustained despite heterogeneity. The pulse-coupled oscillator model can not only be used to describe biological neuronal networks but also cardiac pacemakers, lasers, fireflies, artificial neural networks, social self-organization, and wireless sensor networks. AMS Subject Classification:37N25, 39A06, 39A30, 92B25, 92C20.

A synergistic combination of in vitro electrophysiology and multicompartmental modeling of rat CA1 pyramidal neurons identified TRPM4 channels as major drivers of cholinergic modulation of the firing rate during a triangular current ramp, which emulates the bump in synaptic input received while traversing the place field. In control, fewer spikes at lower frequencies are elicited on the down-ramp compared to the up-ramp due to long-term inactivation of the Na V channel. The cholinergic agonist carbachol (CCh) removes or even reverses this spike rate adaptation, causing more spikes to be elicited on the down-ramp than the up-ramp. CCh application during Schaffer collateral stimulation designed to simulate a ramp produces similar shifts in the center of mass of firing to later in the ramp. The non-specific TRP antagonist flufenamic acid and the TRPM4-specific blockers CBA and 9-phenanthrol, but not the TRPC-specific antagonist SKF96365, reverse the effect of CCh; this implicates the Ca 2+ -activated nonspecific cation current, I CAN , carried by TRPM4 channels. The cholinergic shift of the center of mass of firing is prevented by strong intracellular Ca 2+ buffering but not by antagonists for IP 3 and ryanodine receptors, ruling out a role for known mechanisms of release from intracellular Ca 2+ stores. Pharmacology combined with modeling suggest that [Ca 2+ ] in a nanodomain near the TRPM4 channel is elevated through an unknown source that requires both muscarinic receptor activation and depolarization-induced Ca 2+ influx during the ramp. Activation of the regenerative inward TRPM4 current in the model qualitatively replicates and provides putative underlying mechanisms for the experimental observations.

Parvalbumin-positive (Pvalb(+)) and somatostatin-positive (Sst(+)) cells are the two largest subgroups of inhibitory interneurons. Studies in visual cortex indicate that synaptic connections between Pvalb(+) cells are common while connections between Sst(+) interneurons have not been observed. The inhibitory connectivity and kinetics of these two interneuron subpopulations, however, have not been characterized in medial entorhinal cortex (mEC). Using fluorescence-guided paired recordings in mouse brain slices from interneurons and excitatory cells in layer 2/3 mEC, we found that, unlike neocortical measures, Sst(+) cells inhibit each other, albeit with a lower probability than Pvalb+ cells (18% vs 36% for unidirectional connections). Gap junction connections were also more frequent between Pvalb(+) cells than between Sst(+) cells. Pvalb(+) cells inhibited each other with larger conductances, smaller decay time constants, and shorter delays. Similarly, synaptic connections between Pvalb(+) and excitatory cells were more likely and expressed faster decay times and shorter delays than those between Sst(+) and excitatory cells. Inhibitory cells exhibited smaller synaptic decay time constants between interneurons than on their excitatory targets. Inhibition between interneurons also depressed faster, and to a greater extent. Finally, inhibition onto layer 2 pyramidal and stellate cells originating from Pvalb(+) interneurons were very similar, with no significant differences in connection likelihood, inhibitory amplitude, and decay time. A model of short-term depression fitted to the data indicates that recovery time constants for refilling the available pool are in the range of 50-150 ms and that the fraction of the available pool released on each spike is in the range 0.2-0.5.

Here we present methodology to simulate the electrical activity of dopamineDopamine (DA) neurons by using a freely available software package to numerically integrate a set of coupled nonlinear equations that describe the equivalent circuit that generates the membrane potential, the nonlinear dynamics of channel gating, and a material balance on Ca2+ ions. The general methodology is conductance-based single-neuron computational modelsComputational models. We begin with Hodgkin-Huxley (H-H)-type conductance-based single-compartment models of pacemakingPacemaking in vitro, which is described mathematically as a limit cycle. We illustrate phase plane methods to gain insight into this activity. Next, we address modeling rhythmic burstingBursting activity. To illustrate that the methodology can be extended beyond the H-H formalism in which activation and inactivation gates operate independently of each other, we include a Markov model of a K+ channel in which they are dependent on each other. We then add random synaptic input to the model to illustrate the hypothesized balanced state in dopamineDopamine (DA) neurons, which is quite distinct from the balanced state of neocortical pyramidal neurons. We use this model to explain transient bursts and pauses. A major advantage of models is that parameter sweeps can be conducted quickly to determine the robustness of predicted activity. Finally, we move to a multi-compartmental model that captures the full morphology of a dopamineDopamine (DA) neuron to illustrate the role of the axonAxons initial segment (AIS) in action potentialAction potentials initiation.

The low-threshold L-type calcium channel Ca v 1.3 accelerates the pacemaker rate in the heart, but its functional role for the extended dynamic range of neuronal firing is still unresolved. Here, we show that Ca v 1.3 calcium channels act as unexpectedly simple, full-range linear amplifiers of firing rates for lateral dopamine substantia nigra (DA SN) neurons in mice. This means that they boost in vitro or in vivo firing frequencies between 2 and 50 hertz by about 30%. Furthermore, we demonstrate that clinically relevant, low nanomolar concentrations of the L-type channel inhibitor isradipine selectively reduce the in vivo firing activity of these nigrostriatal DA SN neurons at therapeutic plasma concentrations. Thus, our study identifies the pacemaker function of neuronal Ca v 1.3 channels and provides direct evidence that repurposing dihydropyridines such as isradipine is feasible to selectively modulate the in vivo activity of highly vulnerable DA SN subpopulations in Parkinson’s disease.

Theta and gamma oscillations in the hippocampus have been hypothesized to play a role in the encoding and retrieval of memories. Recently, it was shown that an intrinsic fast gamma mechanism in medial entorhinal cortex can be recruited by optogenetic stimulation at theta frequencies, which can persist with fast excitatory synaptic transmission blocked, suggesting a contribution of interneuronal network gamma (ING). We calibrated the passive and active properties of a 100-neuron model network to capture the range of passive properties and frequency/current relationships of experimentally recorded PV+ neurons in the medial entorhinal cortex (mEC). The strength and probabilities of chemical and electrical synapses were also calibrated using paired recordings, as were the kinetics and short-term depression (STD) of the chemical synapses. Gap junctions that contribute a noticeable fraction of the input resistance were required for synchrony with hyperpolarizing inhibition; these networks exhibited theta-nested high frequency oscillations similar to the putative ING observed experimentally in the optogenetically-driven PV-ChR2 mice. With STD included in the model, the network desynchronized at frequencies above ~200 Hz, so for sufficiently strong drive, fast oscillations were only observed before the peak of the theta. Because hyperpolarizing synapses provide a synchronizing drive that contributes to robustness in the presence of heterogeneity, synchronization decreases as the hyperpolarizing inhibition becomes weaker. In contrast, networks with shunting inhibition required non-physiological levels of gap junctions to synchronize using conduction delays within the measured range.

Many hippocampal CA1 pyramidal cells function as place cells, increasing their firing rate when a specific place field is traversed. The dependence of CA1 place cell firing on position within the place field is asymmetric. We investigated the source of this asymmetry by injecting triangular depolarizing current ramps to approximate the spatially tuned, temporally diffuse depolarizing synaptic input received by these neurons while traversing a place field. Ramps were applied to CA1 pyramidal neurons from male rats in vitro (slice electrophysiology) and in silico (multicompartmental NEURON model). Under control conditions, CA1 neurons fired more action potentials at higher frequencies on the up-ramp versus the down-ramp. This effect was more pronounced for dendritic compared with somatic ramps. We incorporated a four-state Markov scheme for NaV1.6 channels into our model and calibrated the spatial dependence of long-term inactivation according to the literature; this spatial dependence was sufficient to explain the difference in dendritic versus somatic ramps. Long-term inactivation reduced the firing frequency by decreasing open-state occupancy, and reduced spike amplitude during trains by decreasing occupancy in the closed state, which comprises the available pool. PKC activator phorbol-dibutyrate, known to reduce NaV long-term inactivation, removed spike amplitude attenuation in vitro more visibly in dendrites and greatly reduced adaptation, consistent with our hypothesized mechanism. Intracellular application of a peptide inducing long-term NaV inactivation elicited spike amplitude attenuation during spike trains in the soma and greatly enhanced adaptation. Our synergistic experimental/computational approach shows that long-term inactivation of NaV1.6 is a key mechanism of adaptation in CA1 pyramidal cells. SIGNIFICANCE STATEMENT The hippocampus plays an important role in certain types of memory, in part through context-specific firing of “place cells”; these cells were first identified in rodents as being particularly active when an animal is in a specific location in an environment, called the place field of that neuron. In this in vitro/in silico study, we found that long-term inactivation of sodium channels causes adaptation in the firing rate that could potentially skew the firing of CA1 hippocampal pyramidal neurons earlier within a place field. A computational model of the sodium channel revealed differential regulation of spike frequency and amplitude by long-term inactivation, which may be a general mechanism for spike frequency adaptation in the CNS.

Two subpopulations of midbrain dopamine (DA) neurons are known to have different dynamic firing ranges in vitro that correspond to distinct projection targets: the originally identified conventional DA neurons project to the dorsal striatum and the lateral shell of the nucleus accumbens, whereas an atypical DA population with higher maximum firing frequencies projects to prefrontal regions and other limbic regions including the medial shell of nucleus accumbens. Using a computational model, we show that previously identified differences in biophysical properties do not fully account for the larger dynamic range of the atypical population and predict that the major difference is that originally identified conventional cells have larger occupancy of voltage-gated sodium channels in a long-term inactivated state that recovers slowly; stronger sodium and potassium conductances during action potential firing are also predicted for the conventional compared to the atypical DA population. These differences in sodium channel gating imply that longer intervals between spikes are required in the conventional population for full recovery from long-term inactivation induced by the preceding spike, hence the lower maximum frequency. These same differences can also change the bifurcation structure to account for distinct modes of entry into depolarization block: abrupt versus gradual. The model predicted that in cells that have entered depolarization block, it is much more likely that an additional depolarization can evoke an action potential in conventional DA population. New experiments comparing lateral to medial shell projecting neurons confirmed this model prediction, with implications for differential synaptic integration in the two populations.

Thalamocortical neurons (TCNs) play a critical role in the maintenance of thalamocortical oscillations, dysregulation of which can result in certain types of seizures. Precise control over firing rates of TCNs is foundational to these oscillations, yet the transcriptional mechanisms that constrain these firing rates remain elusive. We hypothesized that Shox2 is a transcriptional regulator of ion channels important for TCN function and that loss of Shox2 alters firing frequency and activity, ultimately perturbing thalamocortical oscillations into an epilepsy-prone state. In this study, we used RNA sequencing and quantitative PCR of control and Shox2 knockout mice to determine Shox2-affected genes and revealed a network of ion channel genes important for neuronal firing properties. Protein regulation was confirmed by Western blotting, and electrophysiological recordings showed that Shox2 KO impacted the firing properties of a subpopulation of TCNs. Computational modeling showed that disruption of these conductances in a manner similar to Shox2's effects modulated frequency of oscillations and could convert sleep spindles to near spike and wave activity, which are a hallmark for absence epilepsy. Finally, Shox2 KO mice were more susceptible to pilocarpine-induced seizures. Overall, these results reveal Shox2 as a transcription factor important for TCN function in adult mouse thalamus.

Many hippocampal CA1 pyramidal cells function as place cells, increasing their firing rate when a specific place field is traversed. The dependence of CA1 place cell firing on position within the place field is asymmetric. We investigated the source of this asymmetry by injecting triangular depolarizing current ramps to approximate the spatially-tuned, temporally-diffuse depolarizing synaptic input received by these neurons while traversing a place field. Ramps were applied to CA1 pyramidal neurons from male rats in vitro (slice electrophysiology) and in silico (multi-compartmental NEURON model). Under control conditions, CA1 neurons fired more action potentials at higher frequencies on the up-ramp versus the down-ramp. This effect was more pronounced for dendritic compared to somatic ramps. We incorporated a four-state Markov scheme for Na V 1.6 channels into our model and calibrated the spatial dependence of long-term inactivation according to the literature; this spatial dependence was sufficient to explain the difference in dendritic versus somatic ramps. Long-term inactivation reduced the firing frequency by decreasing open-state occupancy, and reduced spike amplitude during trains by decreasing occupancy in closed states, which comprise the available pool. PKC activator phorbol-dibutyrate, known to reduce Na V long-term inactivation, removed spike amplitude attenuation in vitro more visibly in dendrites and greatly reduced adaptation, consistent with our hypothesized mechanism. Intracellular application of a peptide inducing long-term Na V inactivation elicited spike amplitude attenuation during spike trains in the soma and greatly enhanced adaptation. Our synergistic experimental/computational approach shows that long-term inactivation of Na V 1.6 is a key mechanism of adaptation in CA1 pyramidal cells. in the longevity of occupancy in the long-term inactivated state. We therefore simulated the typical ramp responses recorded experimentally under control conditions in this modified multicompartmental model containing the Markov model for the Na + channel; we also omitted the M-type and SK K + currents, since the above results indicated these currents did not substantially promote firing rate adaptation during the triangular ramp protocol.

All-to-all homogeneous networks of inhibitory neurons synchronize completely under the right conditions; however, many modeling studies have shown that biological levels of heterogeneity disrupt synchrony. Our fundamental scientific question is "how can neurons maintain partial synchrony in the presence of heterogeneity and noise?" A particular subset of strongly interconnected interneurons, the PV+ fast-spiking (FS) basket neurons, are strongly implicated in γ oscillations and in phase locking of nested γ oscillations to theta. Their excitability type apparently varies between brain regions: in CA1 and the dentate gyrus they have type 1 excitability, meaning that they can fire arbitrarily slowly, whereas in the striatum and cortex they have type 2 excitability, meaning that there is a frequency thresh old below which they cannot sustain repetitive firing. We constrained the models to study the effect of excitability type (more precisely bifurcation type) in isolation from all other factors. We use sparsely connected, heterogeneous, noisy networks with synaptic delays to show that synchronization properties, namely the resistance to suppression and the strength of theta phase to γ amplitude coupling, are strongly dependent on the pairing of excitability type with the type of inhibition. Shunting inhibition performs better for type 1 and hyperpolarizing inhibition for type 2. γ Oscillations and their nesting within theta oscillations are thought to subserve cognitive functions like memory encoding and recall; therefore, it is important to understand the contribution of intrinsic properties to these rhythms.