Pyramidal neurons switch from integrators in vitro to resonators under in vivo-like conditions

Contributions of cortical neuron firing patterns, synaptic connectivity, and plasticity to task performance

Neuronal responses during behavior are diverse, ranging from highly reliable 'classical' responses to irregular 'non-classically responsive' firing. While a continuum of response properties is observed across neural systems, little is known about the synaptic origins and contributions of diverse responses to network function, perception, and behavior. To capture the heterogeneous responses measured from auditory cortex of rodents performing a frequency recognition task, we use a novel task-performing spiking recurrent neural network incorporating spike-timing-dependent plasticity. Reliable and irregular units contribute differentially to task performance via output and recurrent connections, respectively. Excitatory plasticity shifts the response distribution while inhibition constrains its diversity. Together both improve task performance with full network engagement. The same local patterns of synaptic inputs predict spiking response properties of network units and auditory cortical neurons from in vivo whole-cell recordings during behavior. Thus, diverse neural responses contribute to network function and emerge from synaptic plasticity rules.

Persistent Interruption in Parvalbumin-Positive Inhibitory Interneurons: Biophysical and Mathematical Mechanisms

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.

Weak coupling of neurons enables very high-frequency and ultra-fast oscillations through the interplay of synchronized phase shifts

Recently, in the past decade, high-frequency oscillations (HFOs), very high-frequency oscillations (VHFOs), and ultra-fast oscillations (UFOs) were reported in epileptic patients with drug-resistant epilepsy. However, to this day, the physiological origin of these events has yet to be understood. Our study establishes a mathematical framework based on bifurcation theory for investigating the occurrence of VHFOs and UFOs in depth EEG signals of patients with focal epilepsy, focusing on the potential role of reduced connection strength between neurons in an epileptic focus. We demonstrate that synchronization of a weakly coupled network can generate very and ultra high-frequency signals detectable by nearby microelectrodes. In particular, we show that a bistability region enables the persistence of phase-shift synchronized clusters of neurons. This phenomenon is observed for different hippocampal neuron models, including Morris-Lecar, Destexhe-Paré, and an interneuron model. The mechanism seems to be robust for small coupling, and it also persists with random noise affecting the external current. Our findings suggest that weakened neuronal connections could contribute to the production of oscillations with frequencies above 1000 Hz, which could advance our understanding of epilepsy pathology and potentially improve treatment strategies. However, further exploration of various coupling types and complex network models is needed.

Persistent Interruption in Parvalbumin Positive Inhibitory Interneurons: Biophysical and Mathematical Mechanisms

Persistent activity in principal cells is a putative mechanism for maintaining memory traces during working memory. We recently demonstrated persistent interruption of firing in fast-spiking parvalbumin-expressing interneurons (PV-INs), a phenomenon which could serve as a substrate for persistent activity in principal cells through disinhibition lasting hundreds of milliseconds. Here, we find that hippocampal CA1 PV-INs exhibit type 2 excitability, like striatal and neocortical PV-INs. Modelling 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 co-existing stable fixed point corresponding to a non-spiking quiescent state. As Kv1 inactivation decays, the trajectory follows the branch of stable fixed points until it crosses a subcritical Hopf bifurcation 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 Hopf bifurcation, 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.

Neuromodulatory effects on synchrony and network reorganization in networks of coupled Kuramoto oscillators

Neuromodulatory processes in the brain can critically change signal processing on a cellular level leading to dramatic changes in network level reorganization. Here, we use coupled non-identical Kuramoto oscillators to investigate how changes in the shape of phase response curves from Type 1 to Type 2, mediated by varying ACh levels, coupled with activity dependent plasticity may alter network reorganization. We first show that when plasticity is absent, the Type 1 networks, as expected, exhibit asynchronous dynamics with oscillators of the highest natural frequency robustly evolving faster in terms of their phase dynamics. At the same time, the Type 2 networks synchronize, with oscillators locked so that the ones with higher natural frequency have a constant phase lead as compared to the ones with lower natural frequency. This relationship establishes a robust mapping between the frequency and oscillators' phases in the network, leading to structure/frequency mapping when plasticity is present. Further we show that while connection plasticity can produce stable synchrony (so called splay states) in Type 1 networks, the structure/frequency reorganization observed in Type 2 networks is not present.

Neuromodulation via muscarinic acetylcholine pathway can facilitate distinct, complementary, and sequential roles for NREM and REM states during sleep-dependent memory consolidation

Across vertebrate species, sleep consists of repeating cycles of NREM followed by REM. However, the respective functions of NREM, REM, and their stereotypic cycling pattern are not well understood. Using a simplified biophysical network model, we show that NREM and REM sleep can play differential and critical roles in memory consolidation primarily regulated, based on state-specific changes in cholinergic signaling. Within this network, decreasing and increasing muscarinic acetylcholine (ACh) signaling during bouts of NREM and REM, respectively, differentially alters neuronal excitability and excitatory/inhibitory balance. During NREM, deactivation of inhibitory neurons leads to network-wide disinhibition and bursts of synchronized activity led by firing in engram neurons. These features strengthen connections from the original engram neurons to less-active network neurons. In contrast, during REM, an increase in network inhibition suppresses firing in all but the most-active excitatory neurons, leading to competitive strengthening/pruning of the memory trace. We tested the predictions of the model against in vivo recordings from mouse hippocampus during active sleep-dependent memory storage. Consistent with modeling results, we find that functional connectivity between CA1 neurons changes differentially at transition from NREM to REM sleep during learning. Returning to the model, we find that an iterative sequence of state-specific activations during NREM/REM cycling is essential for memory storage in the network, serving a critical role during simultaneous consolidation of multiple memories. Together these results provide a testable mechanistic hypothesis for the respective roles of NREM and REM sleep, and their universal relative timing, in memory consolidation.

Significance statement

Using a simplified computational model and in vivo recordings from mouse hippocampus, we show that NREM and REM sleep can play differential roles in memory consolidation. The specific neurophysiological features of the two sleep states allow for expansion of memory traces (during NREM) and prevention of overlap between different memory traces (during REM). These features are likely essential in the context of storing more than one new memory simultaneously within a brain network.

The enigmatic HCN channels: A cellular neurophysiology perspective

What physiological role does a slow hyperpolarization-activated ion channel with mixed cation selectivity play in the fast world of neuronal action potentials that are driven by depolarization? That puzzling question has piqued the curiosity of physiology enthusiasts about the hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which are widely expressed across the body and especially in neurons. In this review, we emphasize the need to assess HCN channels from the perspective of how they respond to time-varying signals, while also accounting for their interactions with other co-expressing channels and receptors. First, we illustrate how the unique structural and functional characteristics of HCN channels allow them to mediate a slow negative feedback loop in the neurons that they express in. We present the several physiological implications of this negative feedback loop to neuronal response characteristics including neuronal gain, voltage sag and rebound, temporal summation, membrane potential resonance, inductive phase lead, spike triggered average, and coincidence detection. Next, we argue that the overall impact of HCN channels on neuronal physiology critically relies on their interactions with other co-expressing channels and receptors. Interactions with other channels allow HCN channels to mediate intrinsic oscillations, earning them the "pacemaker channel" moniker, and to regulate spike frequency adaptation, plateau potentials, neurotransmitter release from presynaptic terminals, and spike initiation at the axonal initial segment. We also explore the impact of spatially non-homogeneous subcellular distributions of HCN channels in different neuronal subtypes and their interactions with other channels and receptors. Finally, we discuss how plasticity in HCN channels is widely prevalent and can mediate different encoding, homeostatic, and neuroprotective functions in a neuron. In summary, we argue that HCN channels form an important class of channels that mediate a diversity of neuronal functions owing to their unique gating kinetics that made them a puzzle in the first place.

Simulations predict differing phase responses to excitation vs. inhibition in theta-resonant pyramidal neurons

Rhythmic activity is ubiquitous in neural systems, with theta-resonant pyramidal neurons integrating rhythmic inputs in many cortical structures. Impedance analysis has been widely used to examine frequency-dependent responses of neuronal membranes to rhythmic inputs, but it assumes that the neuronal membrane is a linear system, requiring the use of small signals to stay in a near-linear regime. However, postsynaptic potentials are often large and trigger nonlinear mechanisms (voltage-gated ion channels). The goals of this work were to 1) develop an analysis method to evaluate membrane responses in this nonlinear domain and 2) explore phase relationships between rhythmic stimuli and subthreshold and spiking membrane potential (Vmemb) responses in models of theta-resonant pyramidal neurons. Responses in these output regimes were asymmetrical, with different phase shifts during hyperpolarizing and depolarizing half-cycles. Suprathreshold theta-rhythmic stimuli produced nonstationary Vmemb responses. Sinusoidal inputs produced "phase retreat": action potentials occurred progressively later in cycles of the input stimulus, resulting from adaptation. Sinusoidal current with increasing amplitude over cycles produced "phase advance": action potentials occurred progressively earlier. Phase retreat, phase advance, and subthreshold phase shifts were modulated by multiple ion channel conductances. Our results suggest differential responses of cortical neurons depending on the frequency of oscillatory input, which will play a role in neuronal responses to shifts in network state. We hypothesize that intrinsic cellular properties complement network properties and contribute to in vivo phase-shift phenomena such as phase precession, seen in place and grid cells, and phase roll, also observed in hippocampal CA1 neurons.NEW & NOTEWORTHY We augmented electrical impedance analysis to characterize phase shifts between large-amplitude current stimuli and nonlinear, asymmetric membrane potential responses. We predict different frequency-dependent phase shifts in response excitation vs. inhibition, as well as shifts in spike timing over multiple input cycles, in theta-resonant pyramidal neurons. We hypothesize that these effects contribute to navigation-related phenomena such as phase precession and phase roll. Our neuron-level hypothesis complements, rather than falsifies, prior network-level explanations of these phenomena.

Low-dimensional models of single neurons: a review

The classical Hodgkin-Huxley (HH) point-neuron model of action potential generation is four-dimensional. It consists of four ordinary differential equations describing the dynamics of the membrane potential and three gating variables associated to a transient sodium and a delayed-rectifier potassium ionic currents. Conductance-based models of HH type are higher-dimensional extensions of the classical HH model. They include a number of supplementary state variables associated with other ionic current types, and are able to describe additional phenomena such as subthreshold oscillations, mixed-mode oscillations (subthreshold oscillations interspersed with spikes), clustering and bursting. In this manuscript we discuss biophysically plausible and phenomenological reduced models that preserve the biophysical and/or dynamic description of models of HH type and the ability to produce complex phenomena, but the number of effective dimensions (state variables) is lower. We describe several representative models. We also describe systematic and heuristic methods of deriving reduced models from models of HH type.

Synchrony-Division Neural Multiplexing: An Encoding Model

Cortical neurons receive mixed information from the collective spiking activities of primary sensory neurons in response to a sensory stimulus. A recent study demonstrated an abrupt increase or decrease in stimulus intensity and the stimulus intensity itself can be respectively represented by the synchronous and asynchronous spikes of S1 neurons in rats. This evidence capitalized on the ability of an ensemble of homogeneous neurons to multiplex, a coding strategy that was referred to as synchrony-division multiplexing (SDM). Although neural multiplexing can be conceived by distinct functions of individual neurons in a heterogeneous neural ensemble, the extent to which nearly identical neurons in a homogeneous neural ensemble encode multiple features of a mixed stimulus remains unknown. Here, we present a computational framework to provide a system-level understanding on how an ensemble of homogeneous neurons enable SDM. First, we simulate SDM with an ensemble of homogeneous conductance-based model neurons receiving a mixed stimulus comprising slow and fast features. Using feature-estimation techniques, we show that both features of the stimulus can be inferred from the generated spikes. Second, we utilize linear nonlinear (LNL) cascade models and calculate temporal filters and static nonlinearities of differentially synchronized spikes. We demonstrate that these filters and nonlinearities are distinct for synchronous and asynchronous spikes. Finally, we develop an augmented LNL cascade model as an encoding model for the SDM by combining individual LNLs calculated for each type of spike. The augmented LNL model reveals that a homogeneous neural ensemble model can perform two different functions, namely, temporal- and rate-coding, simultaneously.

Dynamical properties of neuromorphic Josephson junctions

Neuromorphic computing exploits the dynamical analogy between many physical systems and neuron biophysics. Superconductor systems, in particular, are excellent candidates for neuromorphic devices due to their capacity to operate at great speeds and with low energy dissipation compared to their silicon counterparts. In this paper, we revisit a prior work on Josephson Junction-based neurons to identify the exact dynamical mechanisms underlying the system's neuronlike properties and reveal complex behaviors which are relevant for neurocomputation and the design of superconducting neuromorphic devices. Our paper lies at the intersection of superconducting physics and theoretical neuroscience, both viewed under a common framework-that of nonlinear dynamics theory.

Heterogeneous mechanisms for synchronization of networks of resonant neurons under different E/I balance regimes

Rhythmic synchronization of neuronal firing patterns is a widely present phenomenon in the brain-one that seems to be essential for many cognitive processes. A variety of mechanisms contribute to generation and synchronization of network oscillations, ranging from intrinsic cellular excitability to network mediated effects. However, it is unclear how these mechanisms interact together. Here, using computational modeling of excitatory-inhibitory neural networks, we show that different synchronization mechanisms dominate network dynamics at different levels of excitation and inhibition (i.e. E/I levels) as synaptic strength is systematically varied. Our results show that with low synaptic strength networks are sensitive to external oscillatory drive as a synchronizing mechanism-a hallmark of resonance. In contrast, in a strongly-connected regime, synchronization is driven by network effects via the direct interaction between excitation and inhibition, and spontaneous oscillations and cross-frequency coupling emerge. Unexpectedly, we find that while excitation dominates network synchrony at low excitatory coupling strengths, inhibition dominates at high excitatory coupling strengths. Together, our results provide novel insights into the oscillatory modulation of firing patterns in different excitation/inhibition regimes.

Physiological noise facilitates multiplexed coding of vibrotactile-like signals in somatosensory cortex

Neurons can use different aspects of their spiking to simultaneously represent (multiplex) different features of a stimulus. For example, some pyramidal neurons in primary somatosensory cortex (S1) use the rate and timing of their spikes to, respectively, encode the intensity and frequency of vibrotactile stimuli. Doing so has several requirements. Because they fire at low rates, pyramidal neurons cannot entrain 1:1 with high-frequency (100 to 600 Hz) inputs and, instead, must skip (i.e., not respond to) some stimulus cycles. The proportion of skipped cycles must vary inversely with stimulus intensity for firing rate to encode stimulus intensity. Spikes must phase-lock to the stimulus for spike times (intervals) to encode stimulus frequency, but, in addition, skipping must occur irregularly to avoid aliasing. Using simulations and in vitro experiments in which mouse S1 pyramidal neurons were stimulated with inputs emulating those induced by vibrotactile stimuli, we show that fewer cycles are skipped as stimulus intensity increases, as required for rate coding, and that intrinsic or synaptic noise can induce irregular skipping without disrupting phase locking, as required for temporal coding. This occurs because noise can modulate the reliability without disrupting the precision of spikes evoked by small-amplitude, fast-onset signals. Specifically, in the fluctuation-driven regime associated with sparse spiking, rate and temporal coding are both paradoxically improved by the strong synaptic noise characteristic of the intact cortex. Our results demonstrate that multiplexed coding by S1 pyramidal neurons is not only feasible under in vivo conditions, but that background synaptic noise is actually beneficial.

A dynamic clamp protocol to artificially modify cell capacitance

Dynamics of excitable cells and networks depend on the membrane time constant, set by membrane resistance and capacitance. Whereas pharmacological and genetic manipulations of ionic conductances of excitable membranes are routine in electrophysiology, experimental control over capacitance remains a challenge. Here, we present capacitance clamp, an approach that allows electrophysiologists to mimic a modified capacitance in biological neurons via an unconventional application of the dynamic clamp technique. We first demonstrate the feasibility to quantitatively modulate capacitance in a mathematical neuron model and then confirm the functionality of capacitance clamp in in vitro experiments in granule cells of rodent dentate gyrus with up to threefold virtual capacitance changes. Clamping of capacitance thus constitutes a novel technique to probe and decipher mechanisms of neuronal signaling in ways that were so far inaccessible to experimental electrophysiology.

Kv1 channels regulate variations in spike patterning and temporal reliability in the avian cochlear nucleus angularis

Diverse physiological phenotypes in a neuronal population can broaden the range of computational capabilities within a brain region. The avian cochlear nucleus angularis (NA) contains a heterogeneous population of neurons whose variation in intrinsic properties results in electrophysiological phenotypes with a range of sensitivities to temporally modulated input. The low-threshold potassium conductance (G_KLT) is a key feature of neurons involved in fine temporal structure coding for sound localization, but a role for these channels in intensity or spectrotemporal coding has not been established. To determine whether G_KLT affects the phenotypical variation and temporal properties of NA neurons, we applied dendrotoxin-I (DTX), a potent antagonist of Kv1-type potassium channels, to chick brain stem slices in vitro during whole cell patch-clamp recordings. We found a cell-type specific subset of NA neurons that was sensitive to DTX: single-spiking NA neurons were most profoundly affected, as well as a subset of tonic-firing neurons. Both tonic I (phasic onset bursting) and tonic II (delayed firing) neurons showed DTX sensitivity in their firing rate and phenotypical firing pattern. Tonic III neurons were unaffected. Spike time reliability and fluctuation sensitivity measured in DTX-sensitive NA neurons was also reduced with DTX. Finally, DTX reduced spike threshold adaptation in these neurons, suggesting that G_KLT contributes to the temporal properties that allow coding of rapid changes in the inputs to NA neurons. These results suggest that variation in Kv1 channel expression may be a key factor in functional diversity in the avian cochlear nucleus.NEW & NOTEWORTHY The dendrotoxin-sensitive voltage-gated potassium conductance typically associated with neuronal coincidence detection in the timing pathway for sound localization is demonstrated to affect spiking patterns and temporal input sensitivity in the intensity pathway in the avian auditory brain stem. The Kv1-family channels appear to be present in a subset of cochlear nucleus angularis neurons, regulate spike threshold dynamics underlying high-pass membrane filtering, and contribute to intrinsic firing diversity.

A small, computationally flexible network produces the phenotypic diversity of song recognition in crickets

How neural networks evolved to generate the diversity of species-specific communication signals is unknown. For receivers of the signals, one hypothesis is that novel recognition phenotypes arise from parameter variation in computationally flexible feature detection networks. We test this hypothesis in crickets, where males generate and females recognize the mating songs with a species-specific pulse pattern, by investigating whether the song recognition network in the cricket brain has the computational flexibility to recognize different temporal features. Using electrophysiological recordings from the network that recognizes crucial properties of the pulse pattern on the short timescale in the cricket Gryllus bimaculatus, we built a computational model that reproduces the neuronal and behavioral tuning of that species. An analysis of the model's parameter space reveals that the network can provide all recognition phenotypes for pulse duration and pause known in crickets and even other insects. Phenotypic diversity in the model is consistent with known preference types in crickets and other insects, and arises from computations that likely evolved to increase energy efficiency and robustness of pattern recognition. The model's parameter to phenotype mapping is degenerate - different network parameters can create similar changes in the phenotype - which likely supports evolutionary plasticity. Our study suggests that computationally flexible networks underlie the diverse pattern recognition phenotypes, and we reveal network properties that constrain and support behavioral diversity.

Post-stroke epileptogenesis is associated with altered intrinsic properties of hippocampal pyramidal neurons leading to increased theta resonance

Brain insults like stroke, trauma or infections often lead to blood-brain barrier-dysfunction (BBBd) frequently resulting into epileptogenesis. Affected patients suffer from seizures and cognitive comorbidities that are potentially linked to altered network oscillations. It has been shown that a hippocampal BBBd in rats leads to in vivo seizures and increased power at theta (3-8 Hz), an important type of network oscillations. However, the underlying cellular mechanisms remain poorly understood. At membrane potentials close to the threshold for action potentials (APs) a subpopulation of CA1 pyramidal cells (PCs) displays intrinsic resonant properties due to an interplay of the muscarine-sensitive K⁺-current (I_M) and the persistent Na⁺-current (I_NaP). Such resonant neurons are more excitable and generate more APs when stimulated at theta frequencies, being strong candidates for contributing to hippocampal theta oscillations during epileptogenesis. We tested this hypothesis by characterizing changes in intrinsic properties of hippocampal PCs one week after post-stroke epileptogenesis, a model associated with BBBd, using slice electrophysiology and computer modeling. We find a higher proportion of resonant neurons in BBBd compared to sham animals (47 vs. 29%), accompanied by an increase in their excitability. In contrast, BBBd non-resonant neurons showed a reduced excitability, presented with lower impedance and more positive AP threshold. We identify an increase in I_M combined with either a reduction in I_NaP or an increase in I_Leak as possible mechanisms underlying the observed changes. Our results support the hypothesis that a higher proportion of more excitable resonant neurons in the hippocampus contributes to increased theta oscillations and an increased likelihood of seizures in a model of post-stroke epileptogenesis.

Efficient and robust coding in heterogeneous recurrent networks

Cortical networks show a large heterogeneity of neuronal properties. However, traditional coding models have focused on homogeneous populations of excitatory and inhibitory neurons. Here, we analytically derive a class of recurrent networks of spiking neurons that close to optimally track a continuously varying input online, based on two assumptions: 1) every spike is decoded linearly and 2) the network aims to reduce the mean-squared error between the input and the estimate. From this we derive a class of predictive coding networks, that unifies encoding and decoding and in which we can investigate the difference between homogeneous networks and heterogeneous networks, in which each neurons represents different features and has different spike-generating properties. We find that in this framework, 'type 1' and 'type 2' neurons arise naturally and networks consisting of a heterogeneous population of different neuron types are both more efficient and more robust against correlated noise. We make two experimental predictions: 1) we predict that integrators show strong correlations with other integrators and resonators are correlated with resonators, whereas the correlations are much weaker between neurons with different coding properties and 2) that 'type 2' neurons are more coherent with the overall network activity than 'type 1' neurons.

M-current induced Bogdanov-Takens bifurcation and switching of neuron excitability class

In this work, we consider a general conductance-based neuron model with the inclusion of the acetycholine sensitive, M-current. We study bifurcations in the parameter space consisting of the applied current [Formula: see text], the maximal conductance of the M-current [Formula: see text] and the conductance of the leak current [Formula: see text]. We give precise conditions for the model that ensure the existence of a Bogdanov-Takens (BT) point and show that such a point can occur by varying [Formula: see text] and [Formula: see text]. We discuss the case when the BT point becomes a Bogdanov-Takens-cusp (BTC) point and show that such a point can occur in the three-dimensional parameter space. The results of the bifurcation analysis are applied to different neuronal models and are verified and supplemented by numerical bifurcation diagrams generated using the package MATCONT. We conclude that there is a transition in the neuronal excitability type organised by the BT point and the neuron switches from Class-I to Class-II as conductance of the M-current increases.

Excitability and Threshold Mechanism for Enhanced Neuronal Response Induced by Inhibition Preceding Excitation

Postinhibitory facilitation (PIF) of neural firing presents a paradoxical phenomenon that the inhibitory effect induces enhancement instead of reduction of the firing activity, which plays important roles in sound location of the auditory nervous system, awaited theoretical explanations. In the present paper, excitability and threshold mechanism for the PIF phenomenon is presented in the Morris-Lecar model with type I, II, and III excitabilities. Firstly, compared with the purely excitatory stimulations applied to the steady state, the inhibitory preceding excitatory stimulation to form pairs induces the firing rate increased for type II and III excitabilities instead of type I excitability, when the interval between the inhibitory and excitatory stimulation within each pair is suitable. Secondly, the threshold mechanism for the PIF phenomenon is acquired. For type II and III excitabilities, the inhibitory stimulation induces subthreshold oscillations around the steady state. During the middle and ending phase of the ascending part and the beginning phase of the descending part within a period of the subthreshold oscillations, the threshold to evoke an action potential by an excitatory stimulation becomes weaker, which is the cause for the PIF phenomenon. Last, a theoretical estimation for the range of the interval between the inhibitory and excitatory stimulation for the PIF phenomenon is acquired, which approximates half of the intrinsic period of the subthreshold oscillations for the relatively strong stimulations and becomes narrower for the relatively weak stimulations. The interval for the PIF phenomenon is much shorter for type III excitability, which is closer to the experiment observation, due to the shorter period of the subthreshold oscillations. The results present the excitability and threshold mechanism for the PIF phenomenon, which provide comprehensive and deep explanations to the PIF phenomenon.

Stimulus-induced Alpha Suppression Tracks the Difficulty of Attentional Selection, Not Visual Working Memory Storage

Human alpha-band activity (8-12 Hz) has been proposed to index a variety of mechanisms during visual processing. Here, we distinguished between an account in which alpha suppression indexes selective attention versus an account in which it indexes subsequent working memory storage. We manipulated two aspects of the visual stimuli that perceptual attention is believed to mitigate before working memory storage: the potential interference from distractors and the size of the focus of attention. We found that the magnitude of alpha-band suppression tracked both of these aspects of the visual arrays. Thus, alpha-band activity after stimulus onset is clearly related to how the visual system deploys perceptual attention and appears to be distinct from mechanisms that store target representations in working memory.

Simulations reveal how M-currents and memory-based inputs from CA3 enable single neuron mismatch detection for EC3 inputs to the CA1 subfield of hippocampus

Significant evidence has accumulated to support the hypothesis that hippocampal region CA1 operates as an associative mismatch detector (e.g., Hasselmo ME, Schnell E, Barkai E. J Neurosci 15: 5249-5262, 1995; Duncan K, Curtis C, Davachi L. J Neurosci 29: 131-139, 2009; Kumaran D, Maguire EA. J Neurosci 27: 8517-8524, 2007; Lisman JE, Grace AA. Neuron 46: 703-713, 2005; Lisman JE, Otmakhova NA. Hippocampus 11: 551-568 2001; Lörincz A, Buzsáki G. Ann N Y Acad Sci 911: 83-111, 2000; Meeter M, Murre JMJ, Talamini LM. Hippocampus 14: 722-741, 2004; Schiffer AM, Ahlheim C, Wurm MF, Schubotz RI. PLoS One 7: e36445, 2012; Vinogradova OS. Hippocampus 11: 578-598 2001). CA1 compares predictive synaptic signals from CA3 with synaptic signals from EC3, which reflect actual sensory inputs. The new CA1 pyramidal model presented here shows that the distal-proximal segregation of synaptic inputs from EC3 versus CA3, along with other biophysical features, enable such pyramids to serve as comparators that switch output encoding from a brief burst, for a match, to prolonged tonic spiking, for a mismatch. By including often-overlooked features of CA1 pyramidal neurons, this new model allows simulation of pharmacological effects that can eliminate either the match (phasic mode) response or the mismatch (tonic mode) response. These simulations reveal that dysfunctions can arise from either too much or too little ACh stimulation of the muscarinic receptors that control KCNQ channels. Additionally, a dysfunction caused by administration of an N-methyl-d-aspartate antagonist could be rescued by simultaneous administration of a KCNQ channel agonist, such as retigabine.NEW & NOTEWORTHY Hippocampal region CA1 operates as an associative mismatch detector, comparing predictive signals from CA3 with signals from EC3 reflecting sensory inputs. This new CA1 pyramidal model shows that biophysical features enable these comparators to switch output between brief bursts for matches and tonic spiking for mismatches. This suggests that cognitive learning models (e.g., predictive coding) may require much less match/mismatch circuitry than commonly assumed. Additional simulations illuminate deficits seen in psychiatric disorders and drug-induced states.

Shunting Inhibition Improves Synchronization in Heterogeneous Inhibitory Interneuronal Networks with Type 1 Excitability Whereas Hyperpolarizing Inhibition Is Better for Type 2 Excitability

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.

Different dynamical behaviors induced by slow excitatory feedback for type II and III excitabilities

Neuronal excitability is classified as type I, II, or III, according to the responses of electronic activities, which play different roles. In the present paper, the effect of an excitatory autapse on type III excitability is investigated and compared to type II excitability in the Morris-Lecar model, based on Hopf bifurcation and characteristics of the nullcline. The autaptic current of a fast-decay autapse produces periodic stimulations, and that of a slow-decay autapse highly resembles sustained stimulations. Thus, both fast- and slow-decay autapses can induce a resting state for type II excitability that changes to repetitive firing. However, for type III excitability, a fast-decay autapse can induce a resting state to change to repetitive firing, while a slow-decay autapse can induce a resting state to change to a resting state following a transient spike instead of repetitive spiking, which shows the abnormal phenomenon that a stronger excitatory effect of a slow-decay autapse just induces weaker responses. Our results uncover a novel paradoxical phenomenon of the excitatory effect, and we present potential functions of fast- and slow-decay autapses that are helpful for the alteration and maintenance of type III excitability in the real nervous system related to neuropathic pain or sound localization.

Heterogeneities in intrinsic excitability and frequency-dependent response properties of granule cells across the blades of the rat dentate gyrus

The dentate gyrus (DG), the input gate to the hippocampus proper, is anatomically segregated into three different sectors, namely, the suprapyramidal blade, the crest region, and the infrapyramidal blade. Although there are well-established differences between these sectors in terms of neuronal morphology, connectivity patterns, and activity levels, differences in electrophysiological properties of granule cells within these sectors have remained unexplored. Here, employing somatic whole cell patch-clamp recordings from the rat DG, we demonstrate that granule cells in these sectors manifest considerable heterogeneities in their intrinsic excitability, temporal summation, action potential characteristics, and frequency-dependent response properties. Across sectors, these neurons showed positive temporal summation of their responses to inputs mimicking excitatory postsynaptic currents and showed little to no sag in their voltage responses to pulse currents. Consistently, the impedance amplitude profile manifested low-pass characteristics and the impedance phase profile lacked positive phase values at all measured frequencies and voltages and for all sectors. Granule cells in all sectors exhibited class I excitability, with broadly linear firing rate profiles, and granule cells in the crest region fired significantly fewer action potentials compared with those in the infrapyramidal blade. Finally, we found weak pairwise correlations across the 18 different measurements obtained individually from each of the three sectors, providing evidence that these measurements are indeed reporting distinct aspects of neuronal physiology. Together, our analyses show that granule cells act as integrators of afferent information and emphasize the need to account for the considerable physiological heterogeneities in assessing their roles in information encoding and processing.NEW & NOTEWORTHY We employed whole cell patch-clamp recordings from granule cells in the three subregions of the rat dentate gyrus to demonstrate considerable heterogeneities in their intrinsic excitability, temporal summation, action potential characteristics, and frequency-dependent response properties. Across sectors, granule cells did not express membrane potential resonance, and their impedance profiles lacked inductive phase leads at all measured frequencies. Our analyses also show that granule cells manifest class I excitability characteristics, categorizing them as integrators of afferent information.

Conditioning by subthreshold synaptic input changes the intrinsic firing pattern of CA3 hippocampal neurons

Unlike synaptic strength, intrinsic excitability is assumed to be a stable property of neurons. For example, learning of somatic conductances is generally not incorporated into computational models, and the discharge pattern of neurons in response to test stimuli is frequently used as a basis for phenotypic classification. However, it is increasingly evident that signal processing properties of neurons are more generally plastic on the timescale of minutes. Here we demonstrate that the intrinsic firing patterns of CA3 neurons of the rat hippocampus in vitro undergo rapid long-term plasticity in response to a few minutes of only subthreshold synaptic conditioning. This plasticity on the spike timing could also be induced by intrasomatic injection of subthreshold depolarizing pulses and was blocked by kinase inhibitors, indicating that discharge dynamics are modulated locally. Cluster analysis of firing patterns before and after conditioning revealed systematic transitions toward adapting and intrinsic burst behaviors, irrespective of the patterns initially exhibited by the cells. We used a conductance-based model to decide appropriate pharmacological blockade and found that the observed transitions are likely due to recruitment of low-voltage calcium and Kv7 potassium conductances. We conclude that CA3 neurons adapt their conductance profile to the subthreshold activity of their input, so that their intrinsic firing pattern is not a static signature, but rather a reflection of their history of subthreshold activity. In this way, recurrent output from CA3 neurons may collectively shape the temporal dynamics of their embedding circuits.NEW & NOTEWORTHY Although firing patterns are widely conserved across the animal phyla, it is still a mystery why nerve cells present such diversity of discharge dynamics upon somatic step currents. Adding a new timing dimension to the intrinsic plasticity literature, here we show that CA3 neurons rapidly adapt through the space of known firing patterns in response to the subthreshold signals that they receive from their embedding circuit, potentially adjusting their network processing to the temporal statistics of their circuit.

Acetylcholine Mediates Dynamic Switching Between Information Coding Schemes in Neuronal Networks

Rate coding and phase coding are the two major coding modes seen in the brain. For these two modes, network dynamics must either have a wide distribution of frequencies for rate coding, or a narrow one to achieve stability in phase dynamics for phase coding. Acetylcholine (ACh) is a potent regulator of neural excitability. Acting through the muscarinic receptor, ACh reduces the magnitude of the potassium M-current, a hyperpolarizing current that builds up as neurons fire. The M-current contributes to several excitability features of neurons, becoming a major player in facilitating the transition between Type 1 (integrator) and Type 2 (resonator) excitability. In this paper we argue that this transition enables a dynamic switch between rate coding and phase coding as levels of ACh release change. When a network is in a high ACh state variations in synaptic inputs will lead to a wider distribution of firing rates across the network and this distribution will reflect the network structure or pattern of external input to the network. When ACh is low, network frequencies become narrowly distributed and the structure of a network or pattern of external inputs will be represented through phase relationships between firing neurons. This work provides insights into how modulation of neuronal features influences network dynamics and information processing across brain states.

Spike threshold adaptation diversifies neuronal operating modes in the auditory brain stem

Single neurons function along a spectrum of neuronal operating modes whose properties determine how the output firing activity is generated from synaptic input. The auditory brain stem contains a diversity of neurons, from pure coincidence detectors to pure integrators and those with intermediate properties. We investigated how intrinsic spike initiation mechanisms regulate neuronal operating mode in the avian cochlear nucleus. Although the neurons in one division of the avian cochlear nucleus, nucleus magnocellularis, have been studied in depth, the spike threshold dynamics of the tonically firing neurons of a second division of cochlear nucleus, nucleus angularis (NA), remained unexplained. The input-output functions of tonically firing NA neurons were interrogated with directly injected in vivo-like current stimuli during whole cell patch-clamp recordings in vitro. Increasing the amplitude of the noise fluctuations in the current stimulus enhanced the firing rates in one subset of tonically firing neurons ("differentiators") but not another ("integrators"). We found that spike thresholds showed significantly greater adaptation and variability in the differentiator neurons. A leaky integrate-and-fire neuronal model with an adaptive spike initiation process derived from sodium channel dynamics was fit to the firing responses and could recapitulate >80% of the precise temporal firing across a range of fluctuation and mean current levels. Greater threshold adaptation explained the frequency-current curve changes due to a hyperpolarized shift in the effective adaptation voltage range and longer-lasting threshold adaptation in differentiators. The fine-tuning of the intrinsic properties of different NA neurons suggests they may have specialized roles in spectrotemporal processing.NEW & NOTEWORTHY Avian cochlear nucleus angularis (NA) neurons are responsible for encoding sound intensity for sound localization and spectrotemporal processing. An adaptive spike threshold mechanism fine-tunes a subset of repetitive-spiking neurons in NA to confer coincidence detector-like properties. A model based on sodium channel inactivation properties reproduced the activity via a hyperpolarized shift in adaptation conferring fluctuation sensitivity.

Phase response theory explains cluster formation in sparsely but strongly connected inhibitory neural networks and effects of jitter due to sparse connectivity

We show how to predict whether a neural network will exhibit global synchrony (a one-cluster state) or a two-cluster state based on the assumption of pulsatile coupling and critically dependent upon the phase response curve (PRC) generated by the appropriate perturbation from a partner cluster. Our results hold for a monotonically increasing (meaning longer delays as the phase increases) PRC, which likely characterizes inhibitory fast-spiking basket and cortical low-threshold-spiking interneurons in response to strong inhibition. Conduction delays stabilize synchrony for this PRC shape, whereas they destroy two-cluster states, the former by avoiding a destabilizing discontinuity and the latter by approaching it. With conduction delays, stronger coupling strength can promote a one-cluster state, so the weak coupling limit is not applicable here. We show how jitter can destabilize global synchrony but not a two-cluster state. Local stability of global synchrony in an all-to-all network does not guarantee that global synchrony can be observed in an appropriately scaled sparsely connected network; the basin of attraction can be inferred from the PRC and must be sufficiently large. Two-cluster synchrony is not obviously different from one-cluster synchrony in the presence of noise and may be the actual substrate for oscillations observed in the local field potential (LFP) and the electroencephalogram (EEG) in situations where global synchrony is not possible. Transitions between cluster states may change the frequency of the rhythms observed in the LFP or EEG. Transitions between cluster states within an inhibitory subnetwork may allow more effective recruitment of pyramidal neurons into the network rhythm. NEW & NOTEWORTHY We show that jitter induced by sparse connectivity can destabilize global synchrony but not a two-cluster state with two smaller clusters firing alternately. On the other hand, conduction delays stabilize synchrony and destroy two-cluster states. These results hold if each cluster exhibits a phase response curve similar to one that characterizes fast-spiking basket and cortical low-threshold-spiking cells for strong inhibition. Either a two-cluster or a one-cluster state might provide the oscillatory substrate for neural computations.

Automated Metadata Suggestion During Repository Submission

Knowledge discovery via an informatics resource is constrained by the completeness of the resource, both in terms of the amount of data it contains and in terms of the metadata that exists to describe the data. Increasing completeness in one of these categories risks reducing completeness in the other because manually curating metadata is time consuming and is restricted by familiarity with both the data and the metadata annotation scheme. The diverse interests of a research community may drive a resource to have hundreds of metadata tags with few examples for each making it challenging for humans or machine learning algorithms to learn how to assign metadata tags properly. We demonstrate with ModelDB, a computational neuroscience model discovery resource, that using manually-curated regular-expression based rules can overcome this challenge by parsing existing texts from data providers during user data entry to suggest metadata annotations and prompt them to suggest other related metadata annotations rather than leaving the task to a curator. In the ModelDB implementation, analyzing the abstract identified 6.4 metadata tags per abstract at 79% precision. Using the full-text produced higher recall with low precision (41%), and the title alone produced few (1.3) metadata annotations per entry; we thus recommend data providers use their abstract during upload. Grouping the possible metadata annotations into categories (e.g. cell type, biological topic) revealed that precision and recall for the different text sources varies by category. Given this proof-of-concept, other bioinformatics resources can likewise improve the quality of their metadata by adopting our approach of prompting data uploaders with relevant metadata at the minimal cost of formalizing rules for each potential metadata annotation.

Restoration of Kv7 Channel-Mediated Inhibition Reduces Cued-Reinstatement of Cocaine Seeking

Cocaine addicts display increased sensitivity to drug-associated cues, due in part to changes in the prelimbic prefrontal cortex (PL-PFC). The cellular mechanisms underlying cue-induced reinstatement of cocaine seeking remain unknown. Reinforcement learning for addictive drugs may produce persistent maladaptations in intrinsic excitability within sparse subsets of PFC pyramidal neurons. Using a model of relapse in male rats, we sampled >600 neurons to examine spike frequency adaptation (SFA) and afterhyperpolarizations (AHPs), two systems that attenuate low-frequency inputs to regulate neuronal synchronization. We observed that training to self-administer cocaine or nondrug (sucrose) reinforcers decreased SFA and AHPs in a subpopulation of PL-PFC neurons. Only with cocaine did the resulting hyperexcitability persist through extinction training and increase during reinstatement. In neurons with intact SFA, dopamine enhanced excitability by inhibiting Kv7 potassium channels that mediate SFA. However, dopamine effects were occluded in neurons from cocaine-experienced rats, where SFA and AHPs were reduced. Pharmacological stabilization of Kv7 channels with retigabine restored SFA and Kv7 channel function in neuroadapted cells. When microinjected bilaterally into the PL-PFC 10 min before reinstatement testing, retigabine reduced cue-induced reinstatement of cocaine seeking. Last, using cFos-GFP transgenic rats, we found that the loss of SFA correlated with the expression of cFos-GFP following both extinction and re-exposure to drug-associated cues. Together, these data suggest that cocaine self-administration desensitizes inhibitory Kv7 channels in a subpopulation of PL-PFC neurons. This subpopulation of neurons may represent a persistent neural ensemble responsible for driving drug seeking in response to cues.SIGNIFICANCE STATEMENT Long after the cessation of drug use, cues associated with cocaine still elicit drug-seeking behavior, in part by activation of the prelimbic prefrontal cortex (PL-PFC). The underlying cellular mechanisms governing these activated neurons remain unclear. Using a rat model of relapse to cocaine seeking, we identified a population of PL-PFC neurons that become hyperexcitable following chronic cocaine self-administration. These neurons show persistent loss of spike frequency adaptation, reduced afterhyperpolarizations, decreased sensitivity to dopamine, and reduced Kv7 channel-mediated inhibition. Stabilization of Kv7 channel function with retigabine normalized neuronal excitability, restored Kv7 channel currents, and reduced drug-seeking behavior when administered into the PL-PFC before reinstatement. These data highlight a persistent adaptation in a subset of PL-PFC neurons that may contribute to relapse vulnerability.

Differences in the Electrophysiological Properties of Mouse Somatosensory Layer 2/3 Neurons In Vivo and Slice Stem from Intrinsic Sources Rather than a Network-Generated High Conductance State

Synaptic activity in vivo can potentially alter the integration properties of neurons. Using recordings in awake mice, we targeted somatosensory layer 2/3 pyramidal neurons and compared neuronal properties with those from slices. Pyramidal cells in vivo had lower resistance and gain values, as well as broader spikes and increased spike frequency adaptation compared to the same cells in slices. Increasing conductance in neurons using dynamic clamp to levels observed in vivo, however, did not lessen the differences between in vivo and slice conditions. Further, local application of tetrodotoxin (TTX) in vivo blocked synaptic-mediated membrane voltage fluctuations but had little impact on pyramidal cell membrane input resistance and time constant values. Differences in electrophysiological properties of layer 2/3 neurons in mouse somatosensory cortex, therefore, stem from intrinsic sources separate from synaptic-mediated membrane voltage fluctuations.

Effects of Social Experience on the Habituation Rate of Zebrafish Startle Escape Response: Empirical and Computational Analyses

While the effects of social experience on nervous system function have been extensively investigated in both vertebrate and invertebrate systems, our understanding of how social status differentially affects learning remains limited. In the context of habituation, a well-characterized form of non-associative learning, we investigated how the learning processes differ between socially dominant and subordinate in zebrafish (Danio rerio). We found that social status and frequency of stimulus inputs influence the habituation rate of short latency C-start escape response that is initiated by the Mauthner neuron (M-cell). Socially dominant animals exhibited higher habituation rates compared to socially subordinate animals at a moderate stimulus frequency, but low stimulus frequency eliminated this difference of habituation rates between the two social phenotypes. Moreover, habituation rates of both dominants and subordinates were higher at a moderate stimulus frequency compared to those at a low stimulus frequency. We investigated a potential mechanism underlying these status-dependent differences by constructing a simplified neurocomputational model of the M-cell escape circuit. The computational study showed that the change in total net excitability of the model M-cell was able to replicate the experimental results. At moderate stimulus frequency, the model M-cell with lower total net excitability, that mimicked a dominant-like phenotype, exhibited higher habituation rates. On the other hand, the model with higher total net excitability, that mimicked the subordinate-like phenotype, exhibited lower habituation rates. The relationship between habituation rates and characteristics (frequency and amplitude) of the repeated stimulus were also investigated. We found that habituation rates are decreasing functions of amplitude and increasing functions of frequency while these rates depend on social status (higher for dominants and lower for subordinates). Our results show that social status affects habituative learning in zebrafish, which could be mediated by a summative neuromodulatory input to the M-cell escape circuit, which enables animals to readily learn to adapt to changes in their social environment.

Dopamine terminals from the ventral tegmental area gate intrinsic inhibition in the prefrontal cortex

Spike frequency adaptation (SFA or accommodation) and calcium‐activated potassium channels that underlie after‐hyperpolarization potentials (AHP) regulate repetitive firing of neurons. Precisely how neuromodulators such as dopamine from the ventral tegmental area (VTA) regulate SFA and AHP (together referred to as intrinsic inhibition) in the prefrontal cortex (PFC) remains unclear. Using whole cell electrophysiology, we measured intrinsic inhibition in prelimbic (PL) layer 5 pyramidal cells of male adult rats. Results demonstrate that bath application of dopamine reduced intrinsic inhibition (EC₅₀: 25.0 μmol/L). This dopamine action was facilitated by coapplication of cocaine (1 μmol/L), a blocker of dopamine reuptake. To evaluate VTA dopamine terminals in PFC slices, we transfected VTA dopamine cells of TH::Cre rats in vivo with Cre‐dependent AAVs to express channelrhodopsin‐2 (ChR2) or designer receptors exclusively activated by designer drugs (DREADDS). In PFC slices from these animals, stimulation of VTA terminals with either blue light to activate ChR2 or bath application of clozapine‐N‐oxide (CNO) to activate Gq‐DREADDs produced a similar reduction in intrinsic inhibition in PL neurons. Electrophysiological recordings from cells expressing retrograde fluorescent tracers showed that this plasticity occurs in PL neurons projecting to the accumbens core. Collectively, these data highlight an ability of VTA terminals to gate intrinsic inhibition in the PFC, and under appropriate circumstances, enhance PL neuronal firing. These cellular actions of dopamine may be important for dopamine‐dependent behaviors involving cocaine and cue‐reward associations within cortical–striatal circuits.

The role of neuron-glia interactions in the emergence of ultra-slow oscillations

Ultra-slow cortical oscillatory activity of 1-100 mHz has been recorded in human by electroencephalography and in dissociated cultures of cortical rat neurons, but the underlying mechanisms remain to be elucidated. This study presents a computational model of ultra-slow oscillatory activity based on the interaction between neurons and astrocytes. We predict that the frequency of these oscillations closely depends on activation of astrocytes in the network, which is reflected by oscillations of their intracellular calcium concentrations with periods between tens of seconds and minutes. An increase of intracellular calcium in astrocytes triggers the release of adenosine triphosphate from these cells which may alter transmission at nearby synapses by increasing or decreasing neurotransmitter release. These results provide theoretical support for the emerging awareness of astrocytes as active players in the regulation of neural activity and identify neuron-astrocyte interactions as a potential primary mechanism for the emergence of ultra-slow cortical oscillations.

Theta-frequency selectivity in the somatic spike-triggered average of rat hippocampal pyramidal neurons is dependent on HCN channels

The ability to distill specific frequencies from complex spatiotemporal patterns of afferent inputs is a pivotal functional requirement for neurons residing in networks receiving frequency-multiplexed inputs. Although the expression of theta-frequency subthreshold resonance is established in hippocampal pyramidal neurons, it is not known if their spike initiation dynamics manifest spectral selectivity, or if their intrinsic properties are tuned to process gamma-frequency inputs. Here, we measured the spike-triggered average (STA) of rat hippocampal pyramidal neurons through electrophysiological recordings and quantified spectral selectivity in their spike initiation dynamics and their coincidence detection window (CDW). Our results revealed strong theta-frequency selectivity in the STA, which was also endowed with gamma-range CDW, with prominent neuron-to-neuron variability that manifested distinct pairwise dissociations and correlations with different intrinsic measurements. Furthermore, we demonstrate that the STA and its measurements substantially adapted to the state of the neuron defined by its membrane potential and to the statistics of its afferent inputs. Finally, we tested the effect of pharmacologically blocking the hyperpolarization-activated cyclic-nucleotide-gated (HCN) channels on the STA and found that the STA characteristic frequency reduced significantly to the delta-frequency band after HCN channel blockade. This delta-frequency selectivity in the STA emerged in the absence of subthreshold resonance, which was abolished by HCN channel blockade, thereby confirming computational predictions on the dissociation between these two forms of spectral selectivity. Our results expand the roles of HCN channels to theta-frequency selectivity in the spike initiation dynamics, apart from underscoring the critical role of interactions among different ion channels in regulating neuronal physiology.NEW & NOTEWORTHY We had previously predicted, using computational analyses, that the spike-triggered average (STA) of hippocampal neurons would exhibit theta-frequency (4-10 Hz) spectral selectivity and would manifest coincidence detection capabilities for inputs in the gamma-frequency band (25-150 Hz). Here, we confirmed these predictions through direct electrophysiological recordings of STA from rat CA1 pyramidal neurons and demonstrate that blocking HCN channels reduces the frequency of STA spectral selectivity to the delta-frequency range (0.5-4 Hz).

Transitions between classes of neuronal excitability and bifurcations induced by autapse

Neuronal excitabilities behave as the basic and important dynamics related to the transitions between firing and resting states, and are characterized by distinct bifurcation types and spiking frequency responses. Switches between class I and II excitabilities induced by modulations outside the neuron (for example, modulation to M-type potassium current) have been one of the most concerning issues in both electrophysiology and nonlinear dynamics. In the present paper, we identified switches between 2 classes of excitability and firing frequency responses when an autapse, which widely exists in real nervous systems and plays important roles via self-feedback, is introduced into the Morris-Lecar (ML) model neuron. The transition from class I to class II excitability and from class II to class I spiking frequency responses were respectively induced by the inhibitory and excitatory autapse, which are characterized by changes of bifurcations, frequency responses, steady-state current-potential curves, and nullclines. Furthermore, we identified codimension-1 and -2 bifurcations and the characteristics of the current-potential curve that determine the transitions. Our results presented a comprehensive relationship between 2 classes of neuronal excitability/spiking characterized by different types of bifurcations, along with a novel possible function of autapse or self-feedback control on modulating neuronal excitability.

A Mechanistic End-to-End Concussion Model That Translates Head Kinematics to Neurologic Injury

Past concussion studies have focused on understanding the injury processes occurring on discrete length scales (e.g., tissue-level stresses and strains, cell-level stresses and strains, or injury-induced cellular pathology). A comprehensive approach that connects all length scales and relates measurable macroscopic parameters to neurological outcomes is the first step toward rationally unraveling the complexity of this multi-scale system, for better guidance of future research. This paper describes the development of the first quantitative end-to-end (E2E) multi-scale model that links gross head motion to neurological injury by integrating fundamental elements of tissue and cellular mechanical response with axonal dysfunction. The model quantifies axonal stretch (i.e., tension) injury in the corpus callosum, with axonal functionality parameterized in terms of axonal signaling. An internal injury correlate is obtained by calculating a neurological injury measure (the average reduction in the axonal signal amplitude) over the corpus callosum. By using a neurologically based quantity rather than externally measured head kinematics, the E2E model is able to unify concussion data across a range of exposure conditions and species with greater sensitivity and specificity than correlates based on external measures. In addition, this model quantitatively links injury of the corpus callosum to observed specific neurobehavioral outcomes that reflect clinical measures of mild traumatic brain injury. This comprehensive modeling framework provides a basis for the systematic improvement and expansion of this mechanistic-based understanding, including widening the range of neurological injury estimation, improving concussion risk correlates, guiding the design of protective equipment, and setting safety standards.

Morphology controls how hippocampal CA1 pyramidal neuron responds to uniform electric fields: a biophysical modeling study

Responses of different neurons to electric field (EF) are highly variable, which depends on intrinsic properties of cell type. Here we use multi-compartmental biophysical models to investigate how morphologic features affect EF-induced responses in hippocampal CA1 pyramidal neurons. We find that the basic morphologies of neuronal elements, including diameter, length, bend, branch, and axon terminals, are all correlated with somatic depolarization through altering the current sources or sinks created by applied field. Varying them alters the EF threshold for triggering action potentials (APs), and then determines cell sensitivity to suprathreshold field. Introducing excitatory postsynaptic potential increases cell excitability and reduces morphology-dependent EF firing threshold. It is also shown that applying identical subthreshold EF results in distinct polarizations on cell membrane with different realistic morphologies. These findings shed light on the crucial role of morphologies in determining field-induced neural response from the point of view of biophysical models. The predictions are conducive to better understanding the variability in modulatory effects of EF stimulation at the cellular level, which could also aid the interpretations of how applied fields activate central nervous system neurons and affect relevant circuits.

Qualitative changes in phase-response curve and synchronization at the saddle-node-loop bifurcation

Prominent changes in neuronal dynamics have previously been attributed to a specific switch in onset bifurcation, the Bogdanov-Takens (BT) point. This study unveils another, relevant and so far underestimated transition point: the saddle-node-loop bifurcation, which can be reached by several parameters, including capacitance, leak conductance, and temperature. This bifurcation turns out to induce even more drastic changes in synchronization than the BT transition. This result arises from a direct effect of the saddle-node-loop bifurcation on the limit cycle and hence spike dynamics. In contrast, the BT bifurcation exerts its immediate influence upon the subthreshold dynamics and hence only indirectly relates to spiking. We specifically demonstrate that the saddle-node-loop bifurcation (i) ubiquitously occurs in planar neuron models with a saddle node on invariant cycle onset bifurcation, and (ii) results in a symmetry breaking of the system's phase-response curve. The latter entails an increase in synchronization range in pulse-coupled oscillators, such as neurons. The derived bifurcation structure is of interest in any system for which a relaxation limit is admissible, such as Josephson junctions and chemical oscillators.

Competition between Persistent Na+ and Muscarine-Sensitive K+ Currents Shapes Perithreshold Resonance and Spike Tuning in CA1 Pyramidal Neurons

Neurons from many brain regions display intrinsic subthreshold theta-resonance, responding preferentially to theta-frequency oscillatory stimuli. Resonance may contribute to selective communication among neurons and to orchestrate brain rhythms. CA1 pyramidal neurons receive theta activity, generating place fields. In these neurons the expression of perithreshold frequency preference is controversial, particularly in the spiking regime, with evidence favoring either non-resonant (integrator-like) or resonant behavior. Perithreshold dynamics depends on the persistent Na⁺ current I_NaP developing above −70 mV and the muscarine-sensitive K⁺ current I_M activating above −60 mV. We conducted current and voltage clamp experiments in slices to investigate perithreshold excitability of CA1 neurons under oscillatory stimulation. Around 20% of neurons displayed perithreshold resonance that is expressed in spiking. The remaining neurons (~80%) acted as low-pass filters lacking frequency preference. Paired voltage clamp measurement of I_NaP and I_M showed that perithreshold activation of I_M is in general low while I_NaP is high enough to depolarize neurons toward threshold before resonance expression, explaining the most abundant non-resonant perithreshold behavior. Partial blockade of I_NaP by pharmacological tools or dynamic clamp changed non-resonant to resonant behavior. Furthermore, shifting I_M activation toward hyperpolarized potentials by dynamic clamp also transformed non-resonant neurons into resonant ones. We propose that the relative levels of I_NaP and I_M control perithreshold behavior of CA1 neurons constituting a gating mechanism for theta resonance in the spiking regime. Both currents are regulated by intracellular signaling and neuromodulators which may allow dynamic switching of perithreshold behavior between resonant and non-resonant.

Phasic Firing and Coincidence Detection by Subthreshold Negative Feedback: Divisive or Subtractive or, Better, Both

Phasic neurons typically fire only for a fast-rising input, say at the onset of a step current, but not for steady or slow inputs, a property associated with type III excitability. Phasic neurons can show extraordinary temporal precision for phase locking and coincidence detection. Exemplars are found in the auditory brain stem where precise timing is used in sound localization. Phasicness at the cellular level arises from a dynamic, voltage-gated, negative feedback that can be recruited subthreshold, preventing the neuron from reaching spike threshold if the voltage does not rise fast enough. We consider two mechanisms for phasicness: a low threshold potassium current (subtractive mechanism) and a sodium current with subthreshold inactivation (divisive mechanism). We develop and analyze three reduced models with either divisive or subtractive mechanisms or both to gain insight into the dynamical mechanisms for the potentially high temporal precision of type III-excitable neurons. We compare their firing properties and performance for a range of stimuli. The models have characteristic non-monotonic input-output relations, firing rate vs. input intensity, for either stochastic current injection or Poisson-timed excitatory synaptic conductance trains. We assess performance according to precision of phase-locking and coincidence detection by the models' responses to repetitive packets of unitary excitatory synaptic inputs with more or less temporal coherence. We find that each mechanism contributes features but best performance is attained if both are present. The subtractive mechanism confers extraordinary precision for phase locking and coincidence detection but only within a restricted parameter range when the divisive mechanism of sodium inactivation is inoperative. The divisive mechanism guarantees robustness of phasic properties, without compromising excitability, although with somewhat less precision. Finally, we demonstrate that brief transient inhibition if properly timed can enhance the reliability of firing.

Dopamine Neurons Change the Type of Excitability in Response to Stimuli

The dynamics of neuronal excitability determine the neuron's response to stimuli, its synchronization and resonance properties and, ultimately, the computations it performs in the brain. We investigated the dynamical mechanisms underlying the excitability type of dopamine (DA) neurons, using a conductance-based biophysical model, and its regulation by intrinsic and synaptic currents. Calibrating the model to reproduce low frequency tonic firing results in N-methyl-D-aspartate (NMDA) excitation balanced by γ-Aminobutyric acid (GABA)-mediated inhibition and leads to type I excitable behavior characterized by a continuous decrease in firing frequency in response to hyperpolarizing currents. Furthermore, we analyzed how excitability type of the DA neuron model is influenced by changes in the intrinsic current composition. A subthreshold sodium current is necessary for a continuous frequency decrease during application of a negative current, and the low-frequency "balanced" state during simultaneous activation of NMDA and GABA receptors. Blocking this current switches the neuron to type II characterized by the abrupt onset of repetitive firing. Enhancing the anomalous rectifier Ih current also switches the excitability to type II. Key characteristics of synaptic conductances that may be observed in vivo also change the type of excitability: a depolarized γ-Aminobutyric acid receptor (GABAR) reversal potential or co-activation of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid receptors (AMPARs) leads to an abrupt frequency drop to zero, which is typical for type II excitability. Coactivation of N-methyl-D-aspartate receptors (NMDARs) together with AMPARs and GABARs shifts the type I/II boundary toward more hyperpolarized GABAR reversal potentials. To better understand how altering each of the aforementioned currents leads to changes in excitability profile of DA neuron, we provide a thorough dynamical analysis. Collectively, these results imply that type I excitability in dopamine neurons might be important for low firing rates and fine-tuning basal dopamine levels, while switching excitability to type II during NMDAR and AMPAR activation may facilitate a transient increase in dopamine concentration, as type II neurons are more amenable to synchronization by mutual excitation.

Coding Properties of Three Intrinsically Distinct Retinal Ganglion Cells under Periodic Stimuli: A Computational Study

As the sole output neurons in the retina, ganglion cells play significant roles in transforming visual information into spike trains, and then transmitting them to the higher visual centers. However, coding strategies that retinal ganglion cells (RGCs) adopt to accomplish these processes are not completely clear yet. To clarify these issues, we investigate the coding properties of three types of RGCs (repetitive spiking, tonic firing, and phasic firing) by two different measures (spike-rate and spike-latency). Model results show that for periodic stimuli, repetitive spiking RGC and tonic RGC exhibit similar spike-rate patterns. Their spike- rates decrease gradually with increased stimulus frequency, moreover, variation of stimulus amplitude would change the two RGCs' spike-rate patterns. For phasic RGC, it activates strongly at medium levels of frequency when the stimulus amplitude is low. While if high stimulus amplitude is applied, phasic RGC switches to respond strongly at low frequencies. These results suggest that stimulus amplitude is a prominent factor in regulating RGCs in encoding periodic signals. Similar conclusions can be drawn when analyzes spike-latency patterns of the three RGCs. More importantly, the above phenomena can be accurately reproduced by Hodgkin's three classes of neurons, indicating that RGCs can perform the typical three classes of firing dynamics, depending on the distinctions of ion channel densities. Consequently, model results from the three RGCs may be not specific, but can also applicable to neurons in other brain regions which exhibit part(s) or all of the Hodgkin's three excitabilities.

Callosal dysfunction explains injury sequelae in a computational network model of axonal injury

Mild traumatic brain injury (mTBI) often results in neurobehavioral aberrations such as impaired attention and increased reaction time. Diffusion imaging and postmortem analysis studies suggest that mTBI primarily affects myelinated axons in white matter tracts. In particular, corpus callosum, mediating interhemispheric information exchange, has been shown to be affected in mTBI. Yet little is known about the mechanisms linking the injury of myelinated callosal axons to the neurobehavioral sequelae of mTBI. To address this issue, we devised and studied a large, biologically plausible neuronal network model of cortical tissue. Importantly, the model architecture incorporated intra- and interhemispheric organization, including myelinated callosal axons and distance-dependent axonal conduction delays. In the resting state, the intact model network exhibited several salient features, including alpha-band (8-12 Hz) collective activity with low-frequency irregular spiking of individual neurons. The network model of callosal injury captured several clinical observations, including 1) "slowing down" of the network rhythms, manifested as an increased resting-state theta-to-alpha power ratio, 2) reduced response to attention-like network stimulation, manifested as a reduced spectral power of collective activity, and 3) increased population response time in response to stimulation. Importantly, these changes were positively correlated with injury severity, supporting proposals to use neurobehavioral indices as biomarkers for determining the severity of injury. Our modeling effort helps to understand the role played by the injury of callosal myelinated axons in defining the neurobehavioral sequelae of mTBI.

Resonant Interneurons Can Increase Robustness of Gamma Oscillations

Gamma oscillations are believed to play a critical role in in information processing, encoding, and retrieval. Inhibitory interneuronal network gamma (ING) oscillations may arise from a coupled oscillator mechanism in which individual neurons oscillate or from a population oscillator in which individual neurons fire sparsely and stochastically. All ING mechanisms, including the one proposed herein, rely on alternating waves of inhibition and windows of opportunity for spiking. The coupled oscillator model implemented with Wang-Buzsáki model neurons is not sufficiently robust to heterogeneity in excitatory drive, and therefore intrinsic frequency, to account for in vitro models of ING. Similarly, in a tightly synchronized regime, the stochastic population oscillator model is often characterized by sparse firing, whereas interneurons both in vivo and in vitro do not fire sparsely during gamma, but rather on average every other cycle. We substituted so-called resonator neural models, which exhibit class 2 excitability and postinhibitory rebound (PIR), for the integrators that are typically used. This results in much greater robustness to heterogeneity that actually increases as the average participation in spikes per cycle approximates physiological levels. Moreover, dynamic clamp experiments that show autapse-induced firing in entorhinal cortical interneurons support the idea that PIR can serve as a network gamma mechanism. Furthermore, parvalbumin-positive (PV(+)) cells were much more likely to display both PIR and autapse-induced firing than GAD2(+) cells, supporting the view that PV(+) fast-firing basket cells are more likely to exhibit class 2 excitability than other types of inhibitory interneurons.

SIGNIFICANCE STATEMENT

Gamma oscillations are believed to play a critical role in information processing, encoding, and retrieval. Networks of inhibitory interneurons are thought to be essential for these oscillations. We show that one class of interneurons with an abrupt onset of firing at a threshold frequency may allow more robust synchronization in the presence of noise and heterogeneity. The mechanism for this robustness depends on the intrinsic resonance at this threshold frequency. Moreover, we show experimentally the feasibility of the proposed mechanism and suggest a way to distinguish between this mechanism and another proposed mechanism: that of a stochastic population oscillator independent of the dynamics of individual neurons.

Mild KCC2 Hypofunction Causes Inconspicuous Chloride Dysregulation that Degrades Neural Coding

Disinhibition caused by Cl⁻ dysregulation is implicated in several neurological disorders. This form of disinhibition, which stems primarily from impaired Cl⁻ extrusion through the co-transporter KCC2, is typically identified by a depolarizing shift in GABA reversal potential (E_GABA). Here we show, using computer simulations, that intracellular [Cl⁻] exhibits exaggerated fluctuations during transient Cl⁻ loads and recovers more slowly to baseline when KCC2 level is even modestly reduced. Using information theory and signal detection theory, we show that increased Cl⁻ lability and settling time degrade neural coding. Importantly, these deleterious effects manifest after less KCC2 reduction than needed to produce the gross changes in E_GABA required for detection by most experiments, which assess KCC2 function under weak Cl⁻ load conditions. By demonstrating the existence and functional consequences of “occult” Cl⁻ dysregulation, these results suggest that modest KCC2 hypofunction plays a greater role in neurological disorders than previously believed.

Postnatal development attunes olfactory bulb mitral cells to high-frequency signaling

Mitral cells (MCs) are a major class of principal neurons in the vertebrate olfactory bulb, conveying odor-evoked activity from the peripheral sensory neurons to olfactory cortex. Previous work has described the development of MC morphology and connectivity during the first few weeks of postnatal development. However, little is known about the postnatal development of MC intrinsic biophysical properties. To understand stimulus encoding in the developing olfactory bulb, we have therefore examined the development of MC intrinsic biophysical properties in acute slices from postnatal day (P)7-P35 mice. Across development, we observed systematic changes in passive membrane properties and action potential waveforms consistent with a developmental increase in sodium and potassium conductances. We further observed developmental decreases in hyperpolarization-evoked membrane potential sag and firing regularity, extending recent links between MC sag heterogeneity and firing patterns. We then applied a novel combination of statistical analyses to examine how the evolution of these intrinsic biophysical properties specifically influenced the representation of fluctuating stimuli by MCs. We found that immature MCs responded to frozen fluctuating stimuli with lower firing rates, lower spike-time reliability, and lower between-cell spike-time correlations than more mature MCs. Analysis of spike-triggered averages revealed that these changes in spike timing were driven by a developmental shift from broad integration of inputs to more selective detection of coincident inputs. Consistent with this shift, generalized linear model fits to MC firing responses demonstrated an enhanced encoding of high-frequency stimulus features by mature MCs.