Impact of fast sodium channel inactivation on spike threshold dynamics and synaptic integration

Loss of Postnatal Arx Transcriptional Activity in Parvalbumin Interneurons Reveals Non-cell Autonomous Disturbances in CA1 Pyramidal Cells

Maintenance of proper electrophysiological and connectivity profiles in the adult brain may be a perturbation point in neurodevelopmental disorders (NDDs). How these profiles are maintained within mature circuits is unclear. We recently demonstrated that postnatal ablation of the Aristaless (Arx) homeobox gene in parvalbumin interneurons (PVIs) alone led to dysregulation of their transcriptome and alterations in their functional as well as network properties in the hippocampal cornu Ammoni first region (CA1). Here, we characterized CA1 pyramidal cells (PCs) responses in this conditional knockout (CKO) mouse to further understand the circuit mechanisms by which postnatal Arx expression regulates mature CA1 circuits. Field recordings of network excitability showed that CA1 PC ensembles were less excitable in response to unpaired stimulations but exhibited enhanced excitability in response to paired-pulse stimulations. Whole-cell voltage clamp recordings revealed a significant increase in the frequency of spontaneous inhibitory postsynaptic currents onto PCs. In contrast, excitatory drive from evoked synaptic transmission was reduced while that of inhibitory synaptic transmission was increased. Current clamp recordings showed increase excitability in several sub- and threshold membrane properties that correlated with an increase in the conductance of Na+ current. Our data suggest that, in addition to cell-autonomous disruption in PVIs, loss of Arx postnatal transcriptional activity in PVIs led to complex dysfunctions in PCs in CA1 microcircuits. These non-cell autonomous effects are likely the product of breakdown in feedback and/or feedforward processes and should be considered as fundamental contributors to the circuit mechanisms of NDDs such as Arx-linked early-onset epileptic encephalopathies.

Adaptive spike threshold dynamics associated with sparse spiking of hilar mossy cells are captured by a simple model

Hilar mossy cells (hMCs) in the dentate gyrus (DG) receive inputs from DG granule cells (GCs), CA3 pyramidal cells and inhibitory interneurons, and provide feedback input to GCs. Behavioural and in vivo recording experiments implicate hMCs in pattern separation, navigation and spatial learning. Our experiments link hMC intrinsic excitability to their synaptically evoked in vivo spiking outputs. We performed electrophysiological recordings from DG neurons and found that hMCs displayed an adaptative spike threshold that increased both in proportion to the intensity of injected currents, and in response to spiking itself, returning to baseline over a long time scale, thereby instantaneously limiting their firing rate responses. The hMC activity is additionally limited by a prominent medium after-hyperpolarizing potential (AHP) generated by small conductance K+ channels. We hypothesize that these intrinsic hMC properties are responsible for their low in vivo firing rates. Our findings extend previous studies that compare hMCs, CA3 pyramidal cells and hilar inhibitory cells and provide novel quantitative data that contrast the intrinsic properties of these cell types. We developed a phenomenological exponential integrate-and-fire model that closely reproduces the hMC adaptive threshold nonlinearities with respect to their threshold dependence on input current intensity, evoked spike latency and long-lasting spike-induced increase in spike threshold. Our robust and computationally efficient model is amenable to incorporation into large network models of the DG that will deepen our understanding of the neural bases of pattern separation, spatial navigation and learning. KEY POINTS: Previous studies have shown that hilar mossy cells (hMCs) are implicated in pattern separation and the formation of spatial memory, but how their intrinsic properties relate to their in vivo spiking patterns is still unknown. Here we show that the hMCs display electrophysiological properties that distinguish them from the other hilar cell types including a highly adaptive spike threshold that decays slowly. The spike-dependent increase in threshold combined with an after-hyperpolarizing potential mediated by a slow K+ conductance is hypothesized to be responsible for the low-firing rate of the hMC observed in vivo. The hMC's features are well captured by a modified stochastic exponential integrate-and-fire model that has the unique feature of a threshold intrinsically dependant on both the stimulus intensity and the spiking history. This computational model will allow future work to study how the hMCs can contribute to spatial memory formation and navigation.

Neural synchrony in cortical networks: mechanisms and implications for neural information processing and coding

Synchronization of neuronal discharges on the millisecond scale has long been recognized as a prevalent and functionally important attribute of neural activity. In this article, I review classical concepts and corresponding evidence of the mechanisms that govern the synchronization of distributed discharges in cortical networks and relate those mechanisms to their possible roles in coding and cognitive functions. To accommodate the need for a selective, directed synchronization of cells, I propose that synchronous firing of distributed neurons is a natural consequence of spike-timing-dependent plasticity (STDP) that associates cells repetitively receiving temporally coherent input: the “synchrony through synaptic plasticity” hypothesis. Neurons that are excited by a repeated sequence of synaptic inputs may learn to selectively respond to the onset of this sequence through synaptic plasticity. Multiple neurons receiving coherent input could thus actively synchronize their firing by learning to selectively respond at corresponding temporal positions. The hypothesis makes several predictions: first, the position of the cells in the network, as well as the source of their input signals, would be irrelevant as long as their input signals arrive simultaneously; second, repeating discharge patterns should get compressed until all or some part of the signals are synchronized; and third, this compression should be accompanied by a sparsening of signals. In this way, selective groups of cells could emerge that would respond to some recurring event with synchronous firing. Such a learned response pattern could further be modulated by synchronous network oscillations that provide a dynamic, flexible context for the synaptic integration of distributed signals. I conclude by suggesting experimental approaches to further test this new hypothesis.

Afterhyperpolarization Promotes the Firing of Mitral Cells through a Voltage-Dependent Modification of Action Potential Threshold

In the olfactory bulb, mitral cells (MCs) display a spontaneous firing that is characterized by bursts of action potentials (APs) intermixed with silent periods. Intraburst firing frequency and duration are heterogeneous among MCs and increase with membrane depolarization. By using patch-clamp recording on rat slices, we dissected out the intrinsic properties responsible for this bursting activity. We showed that the threshold of AP generation dynamically changes as a function of the preceding trajectory of the membrane potential. In fact, the AP threshold became more negative when the membrane was hyperpolarized and had a recovery rate inversely proportional to the membrane repolarization rate. Such variations appeared to be produced by changes in the inactivation state of voltage-dependent Na⁺ channels. Thus, AP initiation was favored by hyperpolarizing events, such as negative membrane oscillations or inhibitory synaptic input. After the first AP, the following fast afterhyperpolarization (AHP) brought the threshold to more negative values and then promoted the emission of the following AP. This phenomenon was repeated for each AP of the burst making the fast AHP a regenerative mechanism that sustained the firing, AHP with larger amplitudes and faster repolarizations being associated with larger and higher-frequency bursts. Burst termination was found to be because of the development of a slow repolarization component of the AHP (slow AHP). Overall, the AHP characteristics appeared as a major determinant of the bursting properties.

Similarities in the Biophysical Properties of Spiral-Ganglion and Vestibular-Ganglion Neurons in Neonatal Rats

The membranes of auditory and vestibular afferent neurons each contain diverse groups of ion channels that lead to heterogeneity in their intrinsic biophysical properties. Pioneering work in both auditory- and vestibular-ganglion physiology have individually examined this remarkable diversity, but there are few direct comparisons between the two ganglia. Here the firing patterns recorded by whole-cell patch-clamping in neonatal vestibular- and spiral ganglion neurons are compared. Indicative of an overall heterogeneity in ion channel composition, both ganglia exhibit qualitatively similar firing patterns ranging from sustained-spiking to transient-spiking in response to current injection. The range of resting potentials, voltage thresholds, current thresholds, input-resistances, and first-spike latencies are similarly broad in both ganglion groups. The covariance between several biophysical properties (e.g., resting potential to voltage threshold and their dependence on postnatal age) was similar between the two ganglia. Cell sizes were on average larger and more variable in VGN than in SGN. One sub-group of VGN stood out as having extra-large somata with transient-firing patterns, very low-input resistance, fast first-spike latencies, and required large current amplitudes to induce spiking. Despite these differences, the input resistance per unit area of the large-bodied transient neurons was like that of smaller-bodied transient-firing neurons in both VGN and SGN, thus appearing to be size-scaled versions of other transient-firing neurons. Our analysis reveals that although auditory and vestibular afferents serve very different functions in distinct sensory modalities, their biophysical properties are more closely related by firing pattern and cell size than by sensory modality.

Electrical match between initial segment and somatodendritic compartment for action potential backpropagation in retinal ganglion cells

The action potential of most vertebrate neurons initiates in the axon initial segment (AIS) and is then transmitted to the soma where it is regenerated by somatodendritic sodium channels. For successful transmission, the AIS must produce a strong axial current, so as to depolarize the soma to the threshold for somatic regeneration. Theoretically, this axial current depends on AIS geometry and Na⁺ conductance density. We measured the axial current of mouse retinal ganglion cells using whole cell recordings with post hoc AIS labeling. We found that this current is large, implying high Na⁺ conductance density, and carries a charge that covaries with capacitance so as to depolarize the soma by ∼30 mV. Additionally, we observed that the axial current attenuates strongly with depolarization, consistent with sodium channel inactivation, but temporally broadens so as to preserve the transmitted charge. Thus, the AIS appears to be organized so as to reliably backpropagate the axonal action potential.NEW & NOTEWORTHY We measured the axial current produced at spike initiation by the axon initial segment of mouse retinal ganglion cells. We found that it is a large current, requiring high sodium channel conductance density, which covaries with cell capacitance so as to ensure a ∼30 mV depolarization. During sustained depolarization the current attenuated, but it broadened to preserve somatic depolarization. Thus, properties of the initial segment are adjusted to ensure backpropagation of the axonal action potential.

Monosynaptic inference via finely-timed spikes

Observations of finely-timed spike relationships in population recordings have been used to support partial reconstruction of neural microcircuit diagrams. In this approach, fine-timescale components of paired spike train interactions are isolated and subsequently attributed to synaptic parameters. Recent perturbation studies strengthen the case for such an inference, yet the complete set of measurements needed to calibrate statistical models is unavailable. To address this gap, we study features of pairwise spiking in a large-scale in vivo dataset where presynaptic neurons were explicitly decoupled from network activity by juxtacellular stimulation. We then construct biophysical models of paired spike trains to reproduce the observed phenomenology of in vivo monosynaptic interactions, including both fine-timescale spike-spike correlations and firing irregularity. A key characteristic of these models is that the paired neurons are coupled by rapidly-fluctuating background inputs. We quantify a monosynapse's causal effect by comparing the postsynaptic train with its counterfactual, when the monosynapse is removed. Subsequently, we develop statistical techniques for estimating this causal effect from the pre- and post-synaptic spike trains. A particular focus is the justification and application of a nonparametric separation of timescale principle to implement synaptic inference. Using simulated data generated from the biophysical models, we characterize the regimes in which the estimators accurately identify the monosynaptic effect. A secondary goal is to initiate a critical exploration of neurostatistical assumptions in terms of biophysical mechanisms, particularly with regards to the challenging but arguably fundamental issue of fast, unobservable nonstationarities in background dynamics.

Simple models including energy and spike constraints reproduce complex activity patterns and metabolic disruptions

In this work, we introduce new phenomenological neuronal models (eLIF and mAdExp) that account for energy supply and demand in the cell as well as the inactivation of spike generation how these interact with subthreshold and spiking dynamics. Including these constraints, the new models reproduce a broad range of biologically-relevant behaviors that are identified to be crucial in many neurological disorders, but were not captured by commonly used phenomenological models. Because of their low dimensionality eLIF and mAdExp open the possibility of future large-scale simulations for more realistic studies of brain circuits involved in neuronal disorders. The new models enable both more accurate modeling and the possibility to study energy-associated disorders over the whole time-course of disease progression instead of only comparing the initially healthy status with the final diseased state. These models, therefore, provide new theoretical and computational methods to assess the opportunities of early diagnostics and the potential of energy-centered approaches to improve therapies.

Neurons, even “at rest”, require a constant supply of energy to function. They cannot sustain high-frequency activity over long periods because of regulatory mechanisms, such as adaptation or sodium channels inactivation, and metabolic limitations. These limitations are especially severe in many neuronal disorders, where energy can become insufficient and make the neuronal response change drastically, leading to increased burstiness, network oscillations, or seizures. Capturing such behaviors and impact of energy constraints on them is an essential prerequisite to study disorders such as Parkinson’s disease and epilepsy. However, energy and spiking constraints are not present in any of the standard neuronal models used in computational neuroscience. Here we introduce models that provide a simple and scalable way to account for these features, enabling large-scale theoretical and computational studies of neurological disorders and activity patterns that could not be captured by previously used models. These models provide a way to study energy-associated disorders over the whole time-course of disease progression, and they enable a better assessment of energy-centered approaches to improve therapies.

Refractory density model of cortical direction selectivity: Lagged-nonlagged, transient-sustained, and On-Off thalamic neuron-based mechanisms and intracortical amplification

A biophysically detailed description of the mechanisms of the primary vision is still being developed. We have incorporated a simplified, filter-based description of retino-thalamic visual signal processing into the detailed, conductance-based refractory density description of the neuronal population activity of the primary visual cortex. We compared four mechanisms of the direction selectivity (DS), three of them being based on asymmetrical projections of different types of thalamic neurons to the cortex, distinguishing between (i) lagged and nonlagged, (ii) transient and sustained, and (iii) On and Off neurons. The fourth mechanism implies a lack of subcortical bias and is an epiphenomenon of intracortical interactions between orientation columns. The simulations of the cortical response to moving gratings have verified that first three mechanisms provide DS to an extent compared with experimental data and that the biophysical model realistically reproduces characteristics of the visual cortex activity, such as membrane potential, firing rate, and synaptic conductances. The proposed model reveals the difference between the mechanisms of both the intact and the silenced cortex, favoring the second mechanism. In the fourth case, DS is weaker but significant; it completely vanishes in the silenced cortex.DS in the On-Off mechanism derives from the nonlinear interactions within the orientation map. Results of simulations can help to identify a prevailing mechanism of DS in V1. This is a step towards a comprehensive biophysical modeling of the primary visual system in the frameworks of the population rate coding concept.

A major mechanism that underlies tuning of cortical neurons to the direction of a moving stimulus is still debated. Considering the visual cortex structured with orientation-selective columns, we have realized and compared in our biophysically detailed mathematical model four hypothetical mechanisms of the direction selectivity (DS) known from experiments. The present model accomplishes our previous model that was tuned to experimental data on excitability in slices and reproduces orientation tuning effects in vivo. In simulations, we have found that the convergence of inputs from so-called transient and sustained (or lagged and nonlagged) thalamic neurons in the cortex provides an initial bias for DS, whereas cortical interactions amplify the tuning. In the absence of any bias, DS emerges as an epiphenomenon of the orientation map. In the case of a biased convergence of On- and Off- thalamic inputs, DS emerges with the help of the intracortical interactions on the orientation map, also. Thus, we have proposed a comprehensive description of the primary vision and revealed characteristic features of different mechanisms of DS in the visual cortex with columnar structure.

Axonal Na+ channels detect and transmit levels of input synchrony in local brain circuits

Sensory processing requires mechanisms of fast coincidence detection to discriminate synchronous from asynchronous inputs. Spike threshold adaptation enables such a discrimination but is ineffective in transmitting this information to the network. We show here that presynaptic axonal sodium channels read and transmit precise levels of input synchrony to the postsynaptic cell by modulating the presynaptic action potential (AP) amplitude. As a consequence, synaptic transmission is facilitated at cortical synapses when the presynaptic spike is produced by synchronous inputs. Using dual soma-axon recordings, imaging, and modeling, we show that this facilitation results from enhanced AP amplitude in the axon due to minimized inactivation of axonal sodium channels. Quantifying local circuit activity and using network modeling, we found that spikes induced by synchronous inputs produced a larger effect on network activity than spikes induced by asynchronous inputs. Therefore, this input synchrony-dependent facilitation may constitute a powerful mechanism, regulating synaptic transmission at proximal synapses.

Theoretical relation between axon initial segment geometry and excitability

In most vertebrate neurons, action potentials are triggered at the distal end of the axon initial segment (AIS). Both position and length of the AIS vary across and within neuron types, with activity, development and pathology. What is the impact of AIS geometry on excitability? Direct empirical assessment has proven difficult because of the many potential confounding factors. Here, we carried a principled theoretical analysis to answer this question. We provide a simple formula relating AIS geometry and sodium conductance density to the somatic voltage threshold. A distal shift of the AIS normally produces a (modest) increase in excitability, but we explain how this pattern can reverse if a hyperpolarizing current is present at the AIS, due to resistive coupling with the soma. This work provides a theoretical tool to assess the significance of structural AIS plasticity for electrical function.

Effect of Stimulus-Dependent Spike Timing on Population Coding of Sound Location in the Owl's Auditory Midbrain

In the auditory system, the spectrotemporal structure of acoustic signals determines the temporal pattern of spikes. Here, we investigated this effect in neurons of the barn owl's auditory midbrain (Tyto furcata) that are selective for auditory space and whether it can influence the coding of sound direction. We found that in the nucleus where neurons first become selective to combinations of sound localization cues, reproducibility of spike trains across repeated trials of identical sounds, a metric of across-trial temporal fidelity of spiking patterns evoked by a stimulus, was maximal at the sound direction that elicited the highest firing rate. We then tested the hypothesis that this stimulus-dependent patterning resulted in rate co-modulation of cells with similar frequency and spatial selectivity, driving stimulus-dependent synchrony of population responses. Tetrodes were used to simultaneously record multiple nearby units in the optic tectum (OT), where auditory space is topographically represented. While spiking of neurons in OT showed lower reproducibility across trials compared with upstream nuclei, spike-time synchrony between nearby OT neurons was highest for sounds at their preferred direction. A model of the midbrain circuit explained the relationship between stimulus-dependent reproducibility and synchrony, and demonstrated that this effect can improve the decoding of sound location from the OT output. Thus, stimulus-dependent spiking patterns in the auditory midbrain can have an effect on spatial coding. This study reports a functional connection between spike patterning elicited by spectrotemporal features of a sound and the coding of its location.

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.

Intrinsic temporal tuning of neurons in the optic tectum is shaped by multisensory experience

For a biological neural network to be functional, its neurons need to be connected with synapses of appropriate strength, and each neuron needs to appropriately respond to its synaptic inputs. This second aspect of network tuning is maintained by intrinsic plasticity; yet it is often considered secondary to changes in connectivity and mostly limited to adjustments of overall excitability of each neuron. Here we argue that even nonoscillatory neurons can be tuned to inputs of different temporal dynamics and that they can routinely adjust this tuning to match the statistics of their synaptic activation. Using the dynamic clamp technique, we show that, in the tectum of Xenopus tadpole, neurons become selective for faster inputs when animals are exposed to fast visual stimuli but remain responsive to longer inputs in animals exposed to slower, looming, or multisensory stimulation. We also report a homeostatic cotuning between synaptic and intrinsic temporal properties of individual tectal cells. These results expand our understanding of intrinsic plasticity in the brain and suggest that there may exist an additional dimension of network tuning that has been so far overlooked.NEW & NOTEWORTHY We use dynamic clamp to show that individual neurons in the tectum of Xenopus tadpoles are selectively tuned to either shorter (more synchronous) or longer (less synchronous) synaptic inputs. We also demonstrate that this intrinsic temporal tuning is strongly shaped by sensory experiences. This new phenomenon, which is likely to be mediated by changes in sodium channel inactivation, is bound to have important consequences for signal processing and the development of local recurrent connections.

Brian 2, an intuitive and efficient neural simulator

Brian 2 allows scientists to simply and efficiently simulate spiking neural network models. These models can feature novel dynamical equations, their interactions with the environment, and experimental protocols. To preserve high performance when defining new models, most simulators offer two options: low-level programming or description languages. The first option requires expertise, is prone to errors, and is problematic for reproducibility. The second option cannot describe all aspects of a computational experiment, such as the potentially complex logic of a stimulation protocol. Brian addresses these issues using runtime code generation. Scientists write code with simple and concise high-level descriptions, and Brian transforms them into efficient low-level code that can run interleaved with their code. We illustrate this with several challenging examples: a plastic model of the pyloric network, a closed-loop sensorimotor model, a programmatic exploration of a neuron model, and an auditory model with real-time input.

Cellular and Network Mechanisms May Generate Sparse Coding of Sequential Object Encounters in Hippocampal-Like Circuits

The localization of distinct landmarks plays a crucial role in encoding new spatial memories. In mammals, this function is performed by hippocampal neurons that sparsely encode an animal’s location relative to surrounding objects. Similarly, the dorsolateral pallium (DL) is essential for spatial learning in teleost fish. The DL of weakly electric gymnotiform fish receives both electrosensory and visual input from the preglomerular nucleus (PG), which has been hypothesized to encode the temporal sequence of electrosensory or visual landmark/food encounters. Here, we show that DL neurons in the Apteronotid fish and in the Carassius auratus (goldfish) have a hyperpolarized resting membrane potential (RMP) combined with a high and dynamic spike threshold that increases following each spike. Current-evoked spikes in DL cells are followed by a strong small-conductance calcium-activated potassium channel (SK)-mediated after-hyperpolarizing potential (AHP). Together, these properties prevent high frequency and continuous spiking. The resulting sparseness of discharge and dynamic threshold suggest that DL neurons meet theoretical requirements for generating spatial memory engrams by decoding the landmark/food encounter sequences encoded by PG neurons. Thus, DL neurons in teleost fish may provide a promising, simple system to study the core cell and network mechanisms underlying spatial memory.

Changes in excitability and ion channel expression in neurons of the major pelvic ganglion in female type II diabetic mice

Bladder cystopathy and autonomic dysfunction are common complications of diabetes, and have been associated with changes in ganglionic transmission and some measures of neuronal excitability in male mice. To determine whether type II diabetes also impacts excitability of ganglionic neurons in females, we investigated neuronal excitability and firing properties, as well as underlying ion channel expression, in major pelvic ganglion (MPG) neurons in control, 10-week, and 21-week Lepr^db/db mice. Type II diabetes in Lepr^db/db animals caused a non-linear change in excitability and firing properties of MPG neurons. At 10 weeks, cells exhibited increased excitability as demonstrated by an increased likelihood of firing multiple spikes upon depolarization, decreased rebound spike latency, and overall narrower action potential half-widths as a result of increased depolarization and repolarization slopes. Conversely, at 21 weeks MPG neurons of Lepr^db/db mice reversed these changes, with spiking patterns and action-potential properties largely returning to control levels. These changes are associated with numerous time-specific changes in calcium, sodium, and potassium channel subunit mRNA levels. However, Principal Components Analysis of channel expression patterns revealed that rectification of excitability is not simply a return to control levels, but rather a distinct ion channel expression profile in 21-week Lepr^db/db neurons. These data indicate that type II diabetes can impact the excitability of post-ganglionic, autonomic neurons of female mice, and suggest that the non-linear progression of these properties with diabetes may be the result of compensatory changes in channel expression that act to rectify disrupted firing patterns of Lepr^db/db MPG neurons.

Amyotrophic lateral sclerosis mutant TDP-43 may cause synaptic dysfunction through altered dendritic spine function

Altered cortical excitability and synapse dysfunction are early pathogenic events in amyotrophic lateral sclerosis (ALS) patients and animal models. Recent studies propose an important role for TAR DNA-binding protein 43 (TDP-43), the mislocalization and aggregation of which are key pathological features of ALS. However, the relationship between ALS-linked TDP-43 mutations, excitability and synaptic function is not fully understood. Here, we investigate the role of ALS-linked mutant TDP-43 in synapse formation by examining the morphological, immunocytochemical and excitability profile of transgenic mouse primary cortical pyramidal neurons that over-express human TDP-43^A315T. In TDP-43^A315T cortical neurons, dendritic spine density was significantly reduced compared to wild-type controls. TDP-43^A315T over-expression increased the total levels of the α-amino-3-hydroxy-5-methyl-4-isoxazolepropinionic acid (AMPA) glutamate receptor subunit GluR1, yet the localization of GluR1 to the dendritic spine was reduced. These postsynaptic changes were coupled with a decrease in the amount of the presynaptic marker synaptophysin that colocalized with dendritic spines. Interestingly, action potential generation was reduced in TDP-43^A315T pyramidal neurons. This work reveals a crucial effect of the over-expression mutation TDP-43^A315T on the formation of synaptic structures and the recruitment of GluR1 to the synaptic membrane. This pathogenic effect may be mediated by cytoplasmic mislocalization of TDP-43^A315T. Loss of synaptic GluR1, and reduced excitability within pyramidal neurons, implicates hypoexcitability and attenuated synaptic function in the pathogenic decline of neuronal function in TDP-43-associated ALS. Further studies into the mechanisms underlying AMPA receptor-mediated excitability changes within the ALS cortical circuitry may yield novel therapeutic targets for treatment of this devastating disease.

Summary: Loss of synaptic GluR1, and reduced excitability within pyramidal neurons, implicates hypoexcitability and attenuated synaptic function in the pathogenic decline of neuronal function in TDP-43-associated ALS.

Loss of Neurofascin-186 Disrupts Alignment of AnkyrinG Relative to Its Binding Partners in the Axon Initial Segment

The axon initial segment (AIS) is a specialized region within the proximal portion of the axon that initiates action potentials thanks in large part to an enrichment of sodium channels. The scaffolding protein ankyrinG (AnkG) is essential for the recruitment of sodium channels as well as several other intracellular and extracellular proteins to the AIS. In the present study, we explore the role of the cell adhesion molecule (CAM) neurofascin-186 (NF-186) in arranging the individual molecular components of the AIS in cultured rat hippocampal neurons. Using a CRISPR depletion strategy to ablate NF expression, we found that the loss of NF selectively perturbed AnkG accumulation and its relative proximal distribution within the AIS. We found that the overexpression of sodium channels could restore AnkG accumulation, but not its altered distribution within the AIS without NF present. We go on to show that although the loss of NF altered AnkG distribution, sodium channel function within the AIS remained normal. Taken together, these results demonstrate that the regulation of AnkG and sodium channel accumulation within the AIS can occur independently of one another, potentially mediated by other binding partners such as NF.

Optimal Localist and Distributed Coding of Spatiotemporal Spike Patterns Through STDP and Coincidence Detection

Repeating spatiotemporal spike patterns exist and carry information. Here we investigated how a single spiking neuron can optimally respond to one given pattern (localist coding), or to either one of several patterns (distributed coding, i.e., the neuron's response is ambiguous but the identity of the pattern could be inferred from the response of multiple neurons), but not to random inputs. To do so, we extended a theory developed in a previous paper (Masquelier, 2017), which was limited to localist coding. More specifically, we computed analytically the signal-to-noise ratio (SNR) of a multi-pattern-detector neuron, using a threshold-free leaky integrate-and-fire (LIF) neuron model with non-plastic unitary synapses and homogeneous Poisson inputs. Surprisingly, when increasing the number of patterns, the SNR decreases slowly, and remains acceptable for several tens of independent patterns. In addition, we investigated whether spike-timing-dependent plasticity (STDP) could enable a neuron to reach the theoretical optimal SNR. To this aim, we simulated a LIF equipped with STDP, and repeatedly exposed it to multiple input spike patterns, embedded in equally dense Poisson spike trains. The LIF progressively became selective to every repeating pattern with no supervision, and stopped discharging during the Poisson spike trains. Furthermore, tuning certain STDP parameters, the resulting pattern detectors were optimal. Tens of independent patterns could be learned by a single neuron using a low adaptive threshold, in contrast with previous studies, in which higher thresholds led to localist coding only. Taken together these results suggest that coincidence detection and STDP are powerful mechanisms, fully compatible with distributed coding. Yet we acknowledge that our theory is limited to single neurons, and thus also applies to feed-forward networks, but not to recurrent ones.

Long-term high-intensity sound stimulation inhibits h current (Ih ) in CA1 pyramidal neurons

Afferent neurotransmission to hippocampal pyramidal cells can lead to long-term changes to their intrinsic membrane properties and affect many ion currents. One of the most plastic neuronal currents is the hyperpolarization-activated cationic current (I_h ), which changes in CA1 pyramidal cells in response to many types of physiological and pathological processes, including auditory stimulation. Recently, we demonstrated that long-term potentiation (LTP) in rat hippocampal Schaffer-CA1 synapses is depressed by high-intensity sound stimulation. Here, we investigated whether a long-term high-intensity sound stimulation could affect intrinsic membrane properties of rat CA1 pyramidal neurons. Our results showed that I_h is depressed by long-term high-intensity sound exposure (1 min of 110 dB sound, applied two times per day for 10 days). This resulted in a decreased resting membrane potential, increased membrane input resistance and time constant, and decreased action potential threshold. In addition, CA1 pyramidal neurons from sound-exposed animals fired more action potentials than neurons from control animals; however, this effect was not caused by a decreased I_h . On the other hand, a single episode (1 min) of 110 dB sound stimulation which also inhibits hippocampal LTP did not affect I_h and firing in pyramidal neurons, suggesting that effects on I_h are long-term responses to high-intensity sound exposure. Our results show that prolonged exposure to high-intensity sound affects intrinsic membrane properties of hippocampal pyramidal neurons, mainly by decreasing the amplitude of I_h .

Precisely timed inhibition facilitates action potential firing for spatial coding in the auditory brainstem

The integration of excitatory and inhibitory synaptic inputs is fundamental to neuronal processing. In the mammalian auditory brainstem, neurons compare excitatory and inhibitory inputs from the ipsilateral and contralateral ear, respectively, for sound localization. However, the temporal precision and functional roles of inhibition in this integration process are unclear. Here, we demonstrate by in vivo recordings from the lateral superior olive (LSO) that inhibition controls spiking with microsecond precision throughout high frequency click trains. Depending on the relative timing of excitation and inhibition, neuronal spike probability is either suppressed or-unexpectedly-facilitated. In vitro conductance-clamp LSO recordings establish that a reduction in the voltage threshold for spike initiation due to a prior hyperpolarization results in post-inhibitory facilitation of otherwise sub-threshold synaptic events. Thus, microsecond-precise differences in the arrival of inhibition relative to excitation can facilitate spiking in the LSO, thereby promoting spatial sensitivity during the processing of faint sounds.

Non-Decaying postsynaptics potentials and delayed spikes in hippocampal pyramidal neurons generated by a zero slope conductance created by the persistent Na+ current

The negative slope conductance created by the persistent sodium current (I_NaP) prolongs the decay phase of excitatory postsynaptic potentials (EPSPs). In a recent study, we demonstrated that this effect was due to an increase of the membrane time constant. When the negative slope conductance opposes completely the positive slope conductances of the other currents it creates a zero slope conductance region. In this region the membrane time constant is infinite and the decay phase of the EPSPs is virtually absent. Here we show that non-decaying EPSPs are present in CA1 hippocampal pyramidal cells in the zero slope conductance region, in the suprathreshold range of membrane potential. Na⁺ channel block with tetrodotoxin abolishes the non-decaying EPSPs. Interestingly, the non-decaying EPSPs are observed only in response to artificial excitatory postsynaptic currents (aEPSCs) of small amplitude, and not in response to aEPSCs of big amplitude. We also observed concomitantly delayed spikes with long latencies and high variability only in response to small amplitude aEPSCs. Our results showed that in CA1 pyramidal neurons I_NaP creates non-decaying EPSPs and delayed spikes in the subthreshold range of membrane potentials, which could potentiate synaptic integration of synaptic potentials coming from distal regions of the dendritic tree.

Computational model of interictal discharges triggered by interneurons

Interictal discharges (IIDs) are abnormal waveforms registered in the periods before or between seizures. IIDs that are initiated by GABAergic interneurons have not been mathematically modeled yet. In the present study, a mathematical model that describes the mechanisms of these discharges is proposed. The model is based on the experimental recordings of IIDs in pyramidal neurons of the rat entorhinal cortex and estimations of synaptic conductances during IIDs. IIDs were induced in cortico-hippocampal slices by applying an extracellular solution with 4-aminopyridine, high potassium, and low magnesium concentrations. Two different types of IIDs initiated by interneurons were observed. The first type of IID (IID1) was pure GABAergic. The second type of IID (IID2) was induced by GABAergic excitation and maintained by recurrent interactions of both GABA- and glutamatergic neuronal populations. The model employed the conductance-based refractory density (CBRD) approach, which accurately approximates the firing rate of a population of similar Hodgkin-Huxley-like neurons. The model of coupled excitatory and inhibitory populations includes AMPA, NMDA, and GABA-receptor-mediated synapses and gap junctions. These neurons receive both arbitrary deterministic input and individual colored Gaussian noise. Both types of IIDs were successfully reproduced in the model by setting two different depolarized levels for GABA-mediated current reversal potential. It was revealed that short-term synaptic depression is a crucial factor in ceasing each of the discharges, and it also determines their durations and frequencies.

Spike threshold dynamics in spinal motoneurons during scratching and swimming

KEY POINTS

Action potential threshold can vary depending on firing history and synaptic inputs. We used an ex vivo carapace-spinal cord preparation from adult turtles to study spike threshold dynamics in motoneurons during two distinct types of functional motor behaviour - fictive scratching and fictive swimming. The threshold potential depolarizes by about 10 mV within each burst of spikes generated during scratch and swim network activity and recovers between bursts to a slightly depolarized level. Slow synaptic integration resulting in a wave of membrane potential depolarization is the factor influencing the threshold potential within firing bursts during motor behaviours. Depolarization of the threshold potential decreases the excitability of motoneurons and may provide a mechanism for stabilization of the response of a motoneuron to intense synaptic inputs to maintain the motor commands within an optimal range for muscle activation.

ABSTRACT

During functional spinal neural network activity motoneurons receive intense synaptic input, and this could modulate the threshold for action potential generation, providing the ability to dynamically adjust the excitability and recruitment order for functional needs. In the present study we investigated the dynamics of action potential threshold during motor network activity. Intracellular recordings from spinal motoneurons in an ex vivo carapace-spinal cord preparation from adult turtles were performed during two distinct types of motor behaviour - fictive scratching and fictive swimming. We found that the threshold of the first spike in episodes of scratching and swimming was the lowest. The threshold potential depolarizes by about 10 mV within each burst of spikes generated during scratch and swim network activity and recovers between bursts to a slightly depolarized level. Depolarization of the threshold potential results in decreased excitability of motoneurons. Synaptic inputs do not modulate the threshold of the first action potential during episodes of scratching or of swimming. There is no correlation between changes in spike threshold and interspike intervals within bursts. Slow synaptic integration that results in a wave of membrane potential depolarization rather than fast synaptic events preceding each spike is the factor influencing the threshold potential within firing bursts during motor behaviours.

Calcium-activated SK channels control firing regularity by modulating sodium channel availability in midbrain dopamine neurons

Dopamine neurons in the substantia nigra pars compacta and ventral tegmental area regulate behaviours such as reward-related learning, and motor control. Dysfunction of these neurons is implicated in Schizophrenia, addiction to drugs, and Parkinson’s disease. While some dopamine neurons fire single spikes at regular intervals, others fire irregular single spikes interspersed with bursts. Pharmacological inhibition of calcium-activated potassium (SK) channels increases the variability in their firing pattern, sometimes also increasing the number of spikes fired in bursts, indicating that SK channels play an important role in maintaining dopamine neuron firing regularity and burst firing. However, the exact mechanisms underlying these effects are still unclear. Here, we develop a biophysical model of a dopamine neuron incorporating ion channel stochasticity that enabled the analysis of availability of ion channels in multiple states during spiking. We find that decreased firing regularity is primarily due to a significant decrease in the AHP that in turn resulted in a reduction in the fraction of available voltage-gated sodium channels due to insufficient recovery from inactivation. Our model further predicts that inhibition of SK channels results in a depolarisation of action potential threshold along with an increase in its variability.

Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size

Neural population equations such as neural mass or field models are widely used to study brain activity on a large scale. However, the relation of these models to the properties of single neurons is unclear. Here we derive an equation for several interacting populations at the mesoscopic scale starting from a microscopic model of randomly connected generalized integrate-and-fire neuron models. Each population consists of 50–2000 neurons of the same type but different populations account for different neuron types. The stochastic population equations that we find reveal how spike-history effects in single-neuron dynamics such as refractoriness and adaptation interact with finite-size fluctuations on the population level. Efficient integration of the stochastic mesoscopic equations reproduces the statistical behavior of the population activities obtained from microscopic simulations of a full spiking neural network model. The theory describes nonlinear emergent dynamics such as finite-size-induced stochastic transitions in multistable networks and synchronization in balanced networks of excitatory and inhibitory neurons. The mesoscopic equations are employed to rapidly integrate a model of a cortical microcircuit consisting of eight neuron types, which allows us to predict spontaneous population activities as well as evoked responses to thalamic input. Our theory establishes a general framework for modeling finite-size neural population dynamics based on single cell and synapse parameters and offers an efficient approach to analyzing cortical circuits and computations.

Understanding the brain requires mathematical models on different spatial scales. On the “microscopic” level of nerve cells, neural spike trains can be well predicted by phenomenological spiking neuron models. On a coarse scale, neural activity can be modeled by phenomenological equations that summarize the total activity of many thousands of neurons. Such population models are widely used to model neuroimaging data such as EEG, MEG or fMRI data. However, it is largely unknown how large-scale models are connected to an underlying microscale model. Linking the scales is vital for a correct description of rapid changes and fluctuations of the population activity, and is crucial for multiscale brain models. The challenge is to treat realistic spiking dynamics as well as fluctuations arising from the finite number of neurons. We obtained such a link by deriving stochastic population equations on the mesoscopic scale of 100–1000 neurons from an underlying microscopic model. These equations can be efficiently integrated and reproduce results of a microscopic simulation while achieving a high speed-up factor. We expect that our novel population theory on the mesoscopic scale will be instrumental for understanding experimental data on information processing in the brain, and ultimately link microscopic and macroscopic activity patterns.

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.

Spikelets in Pyramidal Neurons: Action Potentials Initiated in the Axon Initial Segment That Do Not Activate the Soma

Spikelets are small spike-like depolarizations that can be measured in somatic intracellular recordings. Their origin in pyramidal neurons remains controversial. To explain spikelet generation, we propose a novel single-cell mechanism: somato-dendritic input generates action potentials at the axon initial segment that may fail to activate the soma and manifest as somatic spikelets. Using mathematical analysis and numerical simulations of compartmental neuron models, we identified four key factors controlling spikelet generation: (1) difference in firing threshold, (2) impedance mismatch, and (3) electrotonic separation between the soma and the axon initial segment, as well as (4) input amplitude. Because spikelets involve forward propagation of action potentials along the axon while they avoid full depolarization of the somato-dendritic compartments, we conjecture that this mode of operation saves energy and regulates dendritic plasticity while still allowing for a read-out of results of neuronal computations.

Action potentials (APs) are digital, all-or-none signals by which neurons communicate with each other. Therefore, APs are the basis of neural function, yet some of their fundamental features are still not well understood. Here we focus on pyramidal cells, which are the principal neurons in neocortex and hippocampus. According to textbook knowledge, an AP in pyramidal neurons is initiated at the axon initial segment and propagates along the axon to the next cell. Concurrently, the AP also propagates back to the soma and into the dendrites where it might trigger synaptic plasticity, which is the basis of learning and memory. However, besides APs, pyramidal cells sometimes also show somatic spikelets—small depolarizations with an AP-like shape—whose origin remains unclear. Here, we propose that spikelets occur when an AP initiated at the axon initial segment only propagates down the axon, but fails to activate sodium currents in the soma and dendrites. As a result, spikelet firing saves energy, and moreover, might be a means to control synaptic plasticity and thereby control learning and memory.

Spike-Threshold Variability Originated from Separatrix-Crossing in Neuronal Dynamics

The threshold voltage for action potential generation is a key regulator of neuronal signal processing, yet the mechanism of its dynamic variation is still not well described. In this paper, we propose that threshold phenomena can be classified as parameter thresholds and state thresholds. Voltage thresholds which belong to the state threshold are determined by the 'general separatrix' in state space. We demonstrate that the separatrix generally exists in the state space of neuron models. The general form of separatrix was assumed as the function of both states and stimuli and the previously assumed threshold evolving equation versus time is naturally deduced from the separatrix. In terms of neuronal dynamics, the threshold voltage variation, which is affected by different stimuli, is determined by crossing the separatrix at different points in state space. We suggest that the separatrix-crossing mechanism in state space is the intrinsic dynamic mechanism for threshold voltages and post-stimulus threshold phenomena. These proposals are also systematically verified in example models, three of which have analytic separatrices and one is the classic Hodgkin-Huxley model. The separatrix-crossing framework provides an overview of the neuronal threshold and will facilitate understanding of the nature of threshold variability.

Adaptive Spike Threshold Enables Robust and Temporally Precise Neuronal Encoding

Neural processing rests on the intracellular transformation of information as synaptic inputs are translated into action potentials. This transformation is governed by the spike threshold, which depends on the history of the membrane potential on many temporal scales. While the adaptation of the threshold after spiking activity has been addressed before both theoretically and experimentally, it has only recently been demonstrated that the subthreshold membrane state also influences the effective spike threshold. The consequences for neural computation are not well understood yet. We address this question here using neural simulations and whole cell intracellular recordings in combination with information theoretic analysis. We show that an adaptive spike threshold leads to better stimulus discrimination for tight input correlations than would be achieved otherwise, independent from whether the stimulus is encoded in the rate or pattern of action potentials. The time scales of input selectivity are jointly governed by membrane and threshold dynamics. Encoding information using adaptive thresholds further ensures robust information transmission across cortical states i.e. decoding from different states is less state dependent in the adaptive threshold case, if the decoding is performed in reference to the timing of the population response. Results from in vitro neural recordings were consistent with simulations from adaptive threshold neurons. In summary, the adaptive spike threshold reduces information loss during intracellular information transfer, improves stimulus discriminability and ensures robust decoding across membrane states in a regime of highly correlated inputs, similar to those seen in sensory nuclei during the encoding of sensory information.

A neuron is a tiny computer that transforms electrical inputs into electrical outputs. While neurons have been investigated and modeled for many decades, some aspects remain elusive. Recently, it was demonstrated that the membrane (voltage) state of a neuron determines its threshold to spiking. In the present study we asked, what are the consequences of this dependence for the computation the neuron performs. We find that this so called adaptive threshold allows neurons to be more focused on inputs which arrive close in time with other inputs. Also, it allows neurons to represent their information more robustly, such that a readout of their activity is less influenced by the state the brain is in. The present use of information theory provides a solid foundation for these results. We obtained the results primarily in detailed simulations, but performed neural recordings to verify these properties in real neurons. In summary, an adaptive spiking threshold allows neurons to specifically compute robustly with a focus on tight temporal correlations in their input.

Heterogeneous firing rate response of mouse layer V pyramidal neurons in the fluctuation-driven regime

KEY POINTS

We recreated in vitro the fluctuation-driven regime observed at the soma during asynchronous network activity in vivo and we studied the firing rate response as a function of the properties of the membrane potential fluctuations. We provide a simple analytical template that captures the firing response of both pyramidal neurons and various theoretical models. We found a strong heterogeneity in the firing rate response of layer V pyramidal neurons: in particular, individual neurons differ not only in their mean excitability level, but also in their sensitivity to fluctuations. Theoretical modelling suggest that this observed heterogeneity might arise from various expression levels of the following biophysical properties: sodium inactivation, density of sodium channels and spike frequency adaptation.

ABSTRACT

Characterizing the input-output properties of neocortical neurons is of crucial importance for understanding the properties emerging at the network level. In the regime of low-rate irregular firing (such as in the awake state), determining those properties for neocortical cells remains, however, both experimentally and theoretically challenging. Here, we studied this problem using a combination of theoretical modelling and in vitro experiments. We first identified, theoretically, three somatic variables that describe the dynamical state at the soma in this fluctuation-driven regime: the mean, standard deviation and time constant of the membrane potential fluctuations. Next, we characterized the firing rate response of individual layer V pyramidal cells in this three-dimensional space by means of perforated-patch recordings and dynamic clamp in the visual cortex of juvenile mice in vitro. We found that individual neurons strongly differ not only in terms of their excitability, but also, and unexpectedly, in their sensitivities to fluctuations. Finally, using theoretical modelling, we attempted to reproduce these results. The model predicts that heterogeneous levels of biophysical properties such as sodium inactivation, sharpness of sodium activation and spike frequency adaptation account for the observed diversity of firing rate responses. Because the firing rate response will determine population rate dynamics during asynchronous neocortical activity, our results show that cortical populations are functionally strongly inhomogeneous in young mouse visual cortex, which should have important consequences on the strategies of cortical computation at early stages of sensory processing.

Impact of slow K(+) currents on spike generation can be described by an adaptive threshold model

A neuron that is stimulated by rectangular current injections initially responds with a high firing rate, followed by a decrease in the firing rate. This phenomenon is called spike-frequency adaptation and is usually mediated by slow K(+) currents, such as the M-type K(+) current (I M ) or the Ca(2+)-activated K(+) current (I AHP ). It is not clear how the detailed biophysical mechanisms regulate spike generation in a cortical neuron. In this study, we investigated the impact of slow K(+) currents on spike generation mechanism by reducing a detailed conductance-based neuron model. We showed that the detailed model can be reduced to a multi-timescale adaptive threshold model, and derived the formulae that describe the relationship between slow K(+) current parameters and reduced model parameters. Our analysis of the reduced model suggests that slow K(+) currents have a differential effect on the noise tolerance in neural coding.

Enhanced Sensitivity to Rapid Input Fluctuations by Nonlinear Threshold Dynamics in Neocortical Pyramidal Neurons

The way in which single neurons transform input into output spike trains has fundamental consequences for network coding. Theories and modeling studies based on standard Integrate-and-Fire models implicitly assume that, in response to increasingly strong inputs, neurons modify their coding strategy by progressively reducing their selective sensitivity to rapid input fluctuations. Combining mathematical modeling with in vitro experiments, we demonstrate that, in L5 pyramidal neurons, the firing threshold dynamics adaptively adjust the effective timescale of somatic integration in order to preserve sensitivity to rapid signals over a broad range of input statistics. For that, a new Generalized Integrate-and-Fire model featuring nonlinear firing threshold dynamics and conductance-based adaptation is introduced that outperforms state-of-the-art neuron models in predicting the spiking activity of neurons responding to a variety of in vivo-like fluctuating currents. Our model allows for efficient parameter extraction and can be analytically mapped to a Generalized Linear Model in which both the input filter—describing somatic integration—and the spike-history filter—accounting for spike-frequency adaptation—dynamically adapt to the input statistics, as experimentally observed. Overall, our results provide new insights on the computational role of different biophysical processes known to underlie adaptive coding in single neurons and support previous theoretical findings indicating that the nonlinear dynamics of the firing threshold due to Na⁺-channel inactivation regulate the sensitivity to rapid input fluctuations.

Over the last decades, a variety of simplified spiking models have been shown to achieve a surprisingly high performance in predicting the neuronal responses to in vitro somatic current injections. Because of the complex adaptive behavior featured by cortical neurons, this success is however restricted to limited stimulus ranges: model parameters optimized for a specific input regime are often inappropriate to describe the response to input currents with different statistical properties. In the present study, a new spiking neuron model is introduced that captures single-neuron computation over a wide range of input statistics and explains different aspects of the neuronal dynamics within a single framework. Our results indicate that complex forms of single neuron adaptation are mediated by the nonlinear dynamics of the firing threshold and that the input-output transformation performed by cortical pyramidal neurons can be intuitively understood in terms of an enhanced Generalized Linear Model in which both the input filter and the spike-history filter adapt to the input statistics.

Spike timing precision changes with spike rate adaptation in the owl's auditory space map

Spike rate adaptation (SRA) is a continuing change of responsiveness to ongoing stimuli, which is ubiquitous across species and levels of sensory systems. Under SRA, auditory responses to constant stimuli change over time, relaxing toward a long-term rate often over multiple timescales. With more variable stimuli, SRA causes the dependence of spike rate on sound pressure level to shift toward the mean level of recent stimulus history. A model based on subtractive adaptation (Benda J, Hennig RM. J Comput Neurosci 24: 113-136, 2008) shows that changes in spike rate and level dependence are mechanistically linked. Space-specific neurons in the barn owl's midbrain, when recorded under ketamine-diazepam anesthesia, showed these classical characteristics of SRA, while at the same time exhibiting changes in spike timing precision. Abrupt level increases of sinusoidally amplitude-modulated (SAM) noise initially led to spiking at higher rates with lower temporal precision. Spike rate and precision relaxed toward their long-term values with a time course similar to SRA, results that were also replicated by the subtractive model. Stimuli whose amplitude modulations (AMs) were not synchronous across carrier frequency evoked spikes in response to stimulus envelopes of a particular shape, characterized by the spectrotemporal receptive field (STRF). Again, abrupt stimulus level changes initially disrupted the temporal precision of spiking, which then relaxed along with SRA. We suggest that shifts in latency associated with stimulus level changes may differ between carrier frequency bands and underlie decreased spike precision. Thus SRA is manifest not simply as a change in spike rate but also as a change in the temporal precision of spiking.

Experimentally Verified Parameter Sets for Modelling Heterogeneous Neocortical Pyramidal-Cell Populations

Models of neocortical networks are increasingly including the diversity of excitatory and inhibitory neuronal classes. Significant variability in cellular properties are also seen within a nominal neuronal class and this heterogeneity can be expected to influence the population response and information processing in networks. Recent studies have examined the population and network effects of variability in a particular neuronal parameter with some plausibly chosen distribution. However, the empirical variability and covariance seen across multiple parameters are rarely included, partly due to the lack of data on parameter correlations in forms convenient for model construction. To addess this we quantify the heterogeneity within and between the neocortical pyramidal-cell classes in layers 2/3, 4, and the slender-tufted and thick-tufted pyramidal cells of layer 5 using a combination of intracellular recordings, single-neuron modelling and statistical analyses. From the response to both square-pulse and naturalistic fluctuating stimuli, we examined the class-dependent variance and covariance of electrophysiological parameters and identify the role of the h current in generating parameter correlations. A byproduct of the dynamic I-V method we employed is the straightforward extraction of reduced neuron models from experiment. Empirically these models took the refractory exponential integrate-and-fire form and provide an accurate fit to the perisomatic voltage responses of the diverse pyramidal-cell populations when the class-dependent statistics of the model parameters were respected. By quantifying the parameter statistics we obtained an algorithm which generates populations of model neurons, for each of the four pyramidal-cell classes, that adhere to experimentally observed marginal distributions and parameter correlations. As well as providing this tool, which we hope will be of use for exploring the effects of heterogeneity in neocortical networks, we also provide the code for the dynamic I-V method and make the full electrophysiological data set available.

Neurons are the fundamental components of the nervous system and a quantitative description of their properties is a prerequisite to understanding the complex structures they comprise, from microcircuits to networks. Mathematical modelling provides an essential tool to this end and there has been intense effort directed at analysing networks constructed from different classes of neurons. However, even neurons from the same class show a broad variability in parameter values and the distributions and correlations between these parameters are likely to significantly affect network properties. To quantify this variability, we used a combination of intracellular recording, single-neuron modelling, and statistical analysis to measure the physiological variability in pyramidal-cell populations of the neocortex. We employ protocols that measure parameters from both square-pulse and naturalistic stimuli, characterising the perisomatic integration properties of these cells and allowing for the straightforward extraction of mathematically tractable reduced neuron models. We provide algorithms to generate populations of these neuron models that respect the parameter variability and co-variability observed in our experiments. These represent novel tools for exploring heterogeneity in neocortical networks that will be useful for subsequent theoretical and numerical studies. Finally, we make our full electrophysiological dataset available for other research groups to extend and improve on our analysis.

The domain of neuronal firing on a plane of input current and conductance

The activation of neurotransmitter receptors increases the current flow and membrane conductance and thus controls the firing rate of a neuron. In the present work, we justified the two-dimensional representation of a neuronal input by voltage-independent current and conductance and obtained experimentally and numerically a complete input-output (I/O) function. The dependence of the steady-state firing rate on the input current and conductance was studied as a two-parameter I/O function. We employed the dynamic patch clamp technique in slices to get this dependence for the whole domain of two input signals that evoke stationary spike trains in a single neuron (Ω-domain). As found, the Ω-domain is finite and an additional conductance decreases the range of spike-evoking currents. The I/O function has been reproduced in a Hodgkin-Huxley-like model. Among the simulated effects of different factors on the I/O function, including passive and active membrane properties, external conditions and input signal properties, the most interesting were: the shift of the right boundary of the Ω-domain (corresponding to the exCitation block) leftwards due to the decrease of the maximal potassium conductance; and the reduction of the Ω-domain by the decrease of the maximal sodium concentration. As found in experiments and simulations, the Ω-domain is reduced by the decrease of extracellular sodium concentration, by cooling, and by adding slow potassium currents providing interspike interval adaptation; the Ω-domain height is increased by adding color noise. Our modeling data provided a generalization of I/O dependencies that is consistent with previous studies and our experiments. Our results suggest that both current flow and membrane conductance should be taken into account when determining neuronal firing activity.

Contribution of intrinsic motoneuron properties to discharge hysteresis and its estimation based on paired motor unit recordings: a simulation study

Motoneuron activity is strongly influenced by the activation of persistent inward currents (PICs) mediated by voltage-gated sodium and calcium channels. However, the amount of PIC contribution to the activation of human motoneurons can only be estimated indirectly. Simultaneous recordings of pairs of motor units have been used to provide an estimate of the PIC contribution by using the firing rate of the lower threshold unit to provide an estimate of the common synaptic drive to both units, and the difference in firing rate (ΔF) of this lower threshold unit at recruitment and de-recruitment of the higher threshold unit to estimate the PIC contribution to activation of the higher threshold unit. It has recently been suggested that a number of factors other than PIC can contribute to ΔF values, including mechanisms underlying spike frequency adaptation and spike threshold accommodation. In the present study, we used a set of compartmental models representing a sample of 20 motoneurons with a range of thresholds to investigate how several different intrinsic motoneuron properties can potentially contribute to variations in ΔF values. We drove the models with linearly increasing and decreasing noisy conductance commands of different rate of rise and duration and determined the influence of different intrinsic mechanisms on discharge hysteresis (the difference in excitatory drive at recruitment and de-recruitment) and ΔF. Our results indicate that, although other factors can contribute, variations in discharge hysteresis and ΔF values primarily reflect the contribution of dendritic PICs to motoneuron activation.

Biophysical Insights into How Spike Threshold Depends on the Rate of Membrane Potential Depolarization in Type I and Type II Neurons

Dynamic spike threshold plays a critical role in neuronal input-output relations. In many neurons, the threshold potential depends on the rate of membrane potential depolarization (dV/dt) preceding a spike. There are two basic classes of neural excitability, i.e., Type I and Type II, according to input-output properties. Although the dynamical and biophysical basis of their spike initiation has been established, the spike threshold dynamic for each cell type has not been well described. Here, we use a biophysical model to investigate how spike threshold depends on dV/dt in two types of neuron. It is observed that Type II spike threshold is more depolarized and more sensitive to dV/dt than Type I. With phase plane analysis, we show that each threshold dynamic arises from the different separatrix and K+ current kinetics. By analyzing subthreshold properties of membrane currents, we find the activation of hyperpolarizing current prior to spike initiation is a major factor that regulates the threshold dynamics. The outward K+ current in Type I neuron does not activate at the perithresholds, which makes its spike threshold insensitive to dV/dt. The Type II K+ current activates prior to spike initiation and there is a large net hyperpolarizing current at the perithresholds, which results in a depolarized threshold as well as a pronounced threshold dynamic. These predictions are further attested in several other functionally equivalent cases of neural excitability. Our study provides a fundamental description about how intrinsic biophysical properties contribute to the threshold dynamics in Type I and Type II neurons, which could decipher their significant functions in neural coding.

Input-output relation and energy efficiency in the neuron with different spike threshold dynamics

Neuron encodes and transmits information through generating sequences of output spikes, which is a high energy-consuming process. The spike is initiated when membrane depolarization reaches a threshold voltage. In many neurons, threshold is dynamic and depends on the rate of membrane depolarization (dV/dt) preceding a spike. Identifying the metabolic energy involved in neural coding and their relationship to threshold dynamic is critical to understanding neuronal function and evolution. Here, we use a modified Morris-Lecar model to investigate neuronal input-output property and energy efficiency associated with different spike threshold dynamics. We find that the neurons with dynamic threshold sensitive to dV/dt generate discontinuous frequency-current curve and type II phase response curve (PRC) through Hopf bifurcation, and weak noise could prohibit spiking when bifurcation just occurs. The threshold that is insensitive to dV/dt, instead, results in a continuous frequency-current curve, a type I PRC and a saddle-node on invariant circle bifurcation, and simultaneously weak noise cannot inhibit spiking. It is also shown that the bifurcation, frequency-current curve and PRC type associated with different threshold dynamics arise from the distinct subthreshold interactions of membrane currents. Further, we observe that the energy consumption of the neuron is related to its firing characteristics. The depolarization of spike threshold improves neuronal energy efficiency by reducing the overlap of Na(+) and K(+) currents during an action potential. The high energy efficiency is achieved at more depolarized spike threshold and high stimulus current. These results provide a fundamental biophysical connection that links spike threshold dynamics, input-output relation, energetics and spike initiation, which could contribute to uncover neural encoding mechanism.

Fast-onset long-term open-state block of sodium channels by A-type FHFs mediates classical spike accommodation in hippocampal pyramidal neurons

Classical accommodation is a form of spike frequency adaptation in neurons whereby excitatory drive results in action potential output of gradually decreasing frequency. Here we describe an essential molecular component underlying classical accommodation in juvenile mouse hippocampal CA1 pyramidal neurons. A-type isoforms of fibroblast growth factor homologous factors (FHFs) bound to axosomatic voltage-gated sodium channels bear an N-terminal blocking particle that drives some associated channels into a fast-onset, long-term inactivated state. Use-dependent accumulating channel blockade progressively elevates spike voltage threshold and lengthens interspike intervals. The FHF particle only blocks sodium channels from the open state, and mutagenesis studies demonstrate that this particle uses multiple aliphatic and cationic residues to both induce and maintain the long-term inactivated state. The broad expression of A-type FHFs in neurons throughout the vertebrate CNS suggests a widespread role of these sodium channel modulators in the control of neural firing.

Mechanisms of sharp wave initiation and ripple generation

Replay of neuronal activity during hippocampal sharp wave-ripples (SWRs) is essential in memory formation. To understand the mechanisms underlying the initiation of irregularly occurring SWRs and the generation of periodic ripples, we selectively manipulated different components of the CA3 network in mouse hippocampal slices. We recorded EPSCs and IPSCs to examine the buildup of neuronal activity preceding SWRs and analyzed the distribution of time intervals between subsequent SWR events. Our results suggest that SWRs are initiated through a combined refractory and stochastic mechanism. SWRs initiate when firing in a set of spontaneously active pyramidal cells triggers a gradual, exponential buildup of activity in the recurrent CA3 network. We showed that this tonic excitatory envelope drives reciprocally connected parvalbumin-positive basket cells, which start ripple-frequency spiking that is phase-locked through reciprocal inhibition. The synchronized GABA(A) receptor-mediated currents give rise to a major component of the ripple-frequency oscillation in the local field potential and organize the phase-locked spiking of pyramidal cells. Optogenetic stimulation of parvalbumin-positive cells evoked full SWRs and EPSC sequences in pyramidal cells. Even with excitation blocked, tonic driving of parvalbumin-positive cells evoked ripple oscillations. Conversely, optogenetic silencing of parvalbumin-positive cells interrupted the SWRs or inhibited their occurrence. Local drug applications and modeling experiments confirmed that the activity of parvalbumin-positive perisomatic inhibitory neurons is both necessary and sufficient for ripple-frequency current and rhythm generation. These interneurons are thus essential in organizing pyramidal cell activity not only during gamma oscillation, but, in a different configuration, during SWRs.

A Structural Theory of Pitch(1,2,3)

Musical notes can be ordered from low to high along a perceptual dimension called "pitch". A characteristic property of these sounds is their periodic waveform, and periodicity generally correlates with pitch. Thus, pitch is often described as the perceptual correlate of the periodicity of the sound's waveform. However, the existence and salience of pitch also depends in a complex way on other factors, in particular harmonic content. For example, periodic sounds made of high-order harmonics tend to have a weaker pitch than those made of low-order harmonics. Here we examine the theoretical proposition that pitch is the perceptual correlate of the regularity structure of the vibration pattern of the basilar membrane, across place and time-a generalization of the traditional view on pitch. While this proposition also attributes pitch to periodic sounds, we show that it predicts differences between resolved and unresolved harmonic complexes and a complex domain of existence of pitch, in agreement with psychophysical experiments. We also present a possible neural mechanism for pitch estimation based on coincidence detection, which does not require long delays, in contrast with standard temporal models of pitch.

Neuronal adaptation involves rapid expansion of the action potential initiation site

Action potential (AP) generation is the key to information-processing in the brain. Although APs are normally initiated in the axonal initial segment, developmental adaptation or prolonged network activity may alter the initiation site geometry thus affecting cell excitability. Here we find that hippocampal dentate granule cells adapt their spiking threshold to the kinetics of the ongoing dendrosomatic excitatory input by expanding the AP-initiation area away from the soma while also decelerating local axonal spikes. Dual-patch soma–axon recordings combined with axonal Na⁺ and Ca²⁺ imaging and biophysical modelling show that the underlying mechanism involves distance-dependent inactivation of axonal Na⁺ channels due to somatic depolarization propagating into the axon. Thus, the ensuing changes in the AP-initiation zone and local AP propagation could provide activity-dependent control of cell excitability and spiking on a relatively rapid timescale.

Neuronal adaptation to repetitive stimuli is required for the correct functioning of neuronal networks. Here, the authors show that rapid expansion of the axonal spike-initiation site accompanied by local spike deceleration is the cell adaptation mechanism that responds to repetitive excitatory inputs.

Emergence of band-pass filtering through adaptive spiking in the owl's cochlear nucleus

In the visual, auditory, and electrosensory modalities, stimuli are defined by first- and second-order attributes. The fast time-pressure signal of a sound, a first-order attribute, is important, for instance, in sound localization and pitch perception, while its slow amplitude-modulated envelope, a second-order attribute, can be used for sound recognition. Ascending the auditory pathway from ear to midbrain, neurons increasingly show a preference for the envelope and are most sensitive to particular envelope modulation frequencies, a tuning considered important for encoding sound identity. The level at which this tuning property emerges along the pathway varies across species, and the mechanism of how this occurs is a matter of debate. In this paper, we target the transition between auditory nerve fibers and the cochlear nucleus angularis (NA). While the owl's auditory nerve fibers simultaneously encode the fast and slow attributes of a sound, one synapse further, NA neurons encode the envelope more efficiently than the auditory nerve. Using in vivo and in vitro electrophysiology and computational analysis, we show that a single-cell mechanism inducing spike threshold adaptation can explain the difference in neural filtering between the two areas. We show that spike threshold adaptation can explain the increased selectivity to modulation frequency, as input level increases in NA. These results demonstrate that a spike generation nonlinearity can modulate the tuning to second-order stimulus features, without invoking network or synaptic mechanisms.

Spike-threshold adaptation predicted by membrane potential dynamics in vivo

Neurons encode information in sequences of spikes, which are triggered when their membrane potential crosses a threshold. In vivo, the spiking threshold displays large variability suggesting that threshold dynamics have a profound influence on how the combined input of a neuron is encoded in the spiking. Threshold variability could be explained by adaptation to the membrane potential. However, it could also be the case that most threshold variability reflects noise and processes other than threshold adaptation. Here, we investigated threshold variation in auditory neurons responses recorded in vivo in barn owls. We found that spike threshold is quantitatively predicted by a model in which the threshold adapts, tracking the membrane potential at a short timescale. As a result, in these neurons, slow voltage fluctuations do not contribute to spiking because they are filtered by threshold adaptation. More importantly, these neurons can only respond to input spikes arriving together on a millisecond timescale. These results demonstrate that fast adaptation to the membrane potential captures spike threshold variability in vivo.

Neurons spike when their membrane potential exceeds a threshold value, but this value has been shown to be variable in the same neuron recorded in vivo. This variability could reflect noise, or deterministic processes that make the threshold vary with the membrane potential. The second alternative would have important functional consequences. Here, we show that threshold variability is a genuine feature of neurons, which reflects adaptation to the membrane potential at a short timescale, with little contribution from noise. This demonstrates that a deterministic model can predict spikes based only on the membrane potential.

A simple Markov model of sodium channels with a dynamic threshold

Characteristics of action potential generation are important to understanding brain functioning and, thus, must be understood and modeled. It is still an open question what model can describe concurrently the phenomena of sharp spike shape, the spike threshold variability, and the divisive effect of shunting on the gain of frequency-current dependence. We reproduced these three effects experimentally by patch-clamp recordings in cortical slices, but we failed to simulate them by any of 11 known neuron models, including one- and multi-compartment, with Hodgkin-Huxley and Markov equation-based sodium channel approximations, and those taking into account sodium channel subtype heterogeneity. Basing on our voltage-clamp data characterizing the dependence of sodium channel activation threshold on history of depolarization, we propose a 3-state Markov model with a closed-to-open state transition threshold dependent on slow inactivation. This model reproduces the all three phenomena. As a reduction of this model, a leaky integrate-and-fire model with a dynamic threshold also shows the effect of gain reduction by shunt. These results argue for the mechanism of gain reduction through threshold dynamics determined by the slow inactivation of sodium channels.

Predicting spike timing in highly synchronous auditory neurons at different sound levels

A challenge for sensory systems is to encode natural signals that vary in amplitude by orders of magnitude. The spike trains of neurons in the auditory system must represent the fine temporal structure of sounds despite a tremendous variation in sound level in natural environments. It has been shown in vitro that the transformation from dynamic signals into precise spike trains can be accurately captured by simple integrate-and-fire models. In this work, we show that the in vivo responses of cochlear nucleus bushy cells to sounds across a wide range of levels can be precisely predicted by deterministic integrate-and-fire models with adaptive spike threshold. Our model can predict both the spike timings and the firing rate in response to novel sounds, across a large input level range. A noisy version of the model accounts for the statistical structure of spike trains, including the reliability and temporal precision of responses. Spike threshold adaptation was critical to ensure that predictions remain accurate at different levels. These results confirm that simple integrate-and-fire models provide an accurate phenomenological account of spike train statistics and emphasize the functional relevance of spike threshold adaptation.