Active subthreshold dendritic conductances shape the local field potential

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.

Structural and functional changes of deep layer pyramidal neurons surrounding microelectrode arrays implanted in rat motor cortex

Devices capable of recording or stimulating neuronal signals have created new opportunities to understand normal physiology and treat sources of pathology in the brain. However, it is possible that the tissue response to implanted electrodes may influence the nature of the signals detected or stimulated. In this study, we characterized structural and functional changes in deep layer pyramidal neurons surrounding silicon or polyimide-based electrodes implanted in the motor cortex of rats. Devices were captured in 300 µm-thick tissue slices collected at the 1 or 6 week time point post-implantation, and individual neurons were assessed using a combination of whole-cell electrophysiology and 2-photon imaging. We observed disrupted dendritic arbors and a significant reduction in spine densities in neurons surrounding devices. These effects were accompanied by a decrease in the frequency of spontaneous excitatory post-synaptic currents, a reduction in sag amplitude, an increase in spike frequency adaptation, and an increase in filopodia density. We hypothesize that the effects observed in this study may contribute to the signal loss and instability that often accompany chronically implanted electrodes. STATEMENT OF SIGNIFICANCE: Implanted electrodes in the brain can be used to treat sources of pathology and understand normal physiology by recording or stimulating electrical signals generated by local neurons. However, a foreign body response following implantation undermines the performance of these devices. While several studies have investigated the biological mechanisms of device-tissue interactions through histology, transcriptomics, and imaging, our study is the first to directly interrogate effects on the function of neurons surrounding electrodes using single-cell electrophysiology. Additionally, we provide new, detailed assessments of the impacts of electrodes on the dendritic structure and spine morphology of neurons, and we assess effects for both traditional (silicon) and newer polymer electrode materials. These results reveal new potential mechanisms of electrode-tissue interactions.

Degeneracy in epilepsy: multiple routes to hyperexcitable brain circuits and their repair

Due to its complex and multifaceted nature, developing effective treatments for epilepsy is still a major challenge. To deal with this complexity we introduce the concept of degeneracy to the field of epilepsy research: the ability of disparate elements to cause an analogous function or malfunction. Here, we review examples of epilepsy-related degeneracy at multiple levels of brain organisation, ranging from the cellular to the network and systems level. Based on these insights, we outline new multiscale and population modelling approaches to disentangle the complex web of interactions underlying epilepsy and to design personalised multitarget therapies.

Interictal localization of the epileptogenic zone: Utilizing the observed resonance behavior in the spectral band of surrounding inhibition

Introduction

The gold standard for identification of the epileptogenic zone (EZ) continues to be the visual inspection of electrographic changes around seizures' onset by experienced electroencephalography (EEG) readers. Development of an epileptogenic focus localization tool that can delineate the EZ from analysis of interictal (seizure-free) periods is still an open question of great significance for improved diagnosis (e.g., presurgical evaluation) and treatment of epilepsy (e.g., surgical outcome).

Methods

We developed an EZ interictal localization algorithm (EZILA) based on novel analysis of intracranial EEG (iEEG) using a univariate periodogram-type power measure, a straight-forward ranking approach, a robust dimensional reduction method and a clustering technique. Ten patients with temporal and extra temporal lobe epilepsies, and matching the inclusion criteria of having iEEG recordings at the epilepsy monitoring unit (EMU) and being Engel Class I ≥12 months post-surgery, were recruited in this study.

Results

In a nested k-fold cross validation statistical framework, EZILA assigned the highest score to iEEG channels within the EZ in all patients (10/10) during the first hour of the iEEG recordings and up to their first typical clinical seizure in the EMU (i.e., early interictal period). To further validate EZILA's performance, data from two new (Engel Class I) patients were analyzed in a double-blinded fashion; the EZILA successfully localized iEEG channels within the EZ from interictal iEEG in both patients.

Discussion

Out of the sampled brain regions, iEEG channels in the EZ were most frequently and maximally active in seizure-free (interictal) periods across patients in specific narrow gamma frequency band (∼60-80 Hz), which we have termed focal frequency band (FFB). These findings are consistent with the hypothesis that the EZ may interictally be regulated (controlled) by surrounding inhibitory neurons with resonance characteristics within this narrow gamma band.

Excitatory and inhibitory effects of HCN channel modulation on excitability of layer V pyramidal cells

Dendrites of cortical pyramidal cells are densely populated by hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, a.k.a. Ih channels. Ih channels are targeted by multiple neuromodulatory pathways, and thus are one of the key ion-channel populations regulating the pyramidal cell activity. Previous observations and theories attribute opposing effects of the Ih channels on neuronal excitability due to their mildly hyperpolarized reversal potential. These effects are difficult to measure experimentally due to the fine spatiotemporal landscape of the Ih activity in the dendrites, but computational models provide an efficient tool for studying this question in a reduced but generalizable setting. In this work, we build upon existing biophysically detailed models of thick-tufted layer V pyramidal cells and model the effects of over- and under-expression of Ih channels as well as their neuromodulation. We show that Ih channels facilitate the action potentials of layer V pyramidal cells in response to proximal dendritic stimulus while they hinder the action potentials in response to distal dendritic stimulus at the apical dendrite. We also show that the inhibitory action of the Ih channels in layer V pyramidal cells is due to the interactions between Ih channels and a hot zone of low voltage-activated Ca2+ channels at the apical dendrite. Our simulations suggest that a combination of Ih-enhancing neuromodulation at the proximal part of the apical dendrite and Ih-inhibiting modulation at the distal part of the apical dendrite can increase the layer V pyramidal excitability more than either of the two alone. Our analyses uncover the effects of Ih-channel neuromodulation of layer V pyramidal cells at a single-cell level and shed light on how these neurons integrate information and enable higher-order functions of the brain.

Brain signal predictions from multi-scale networks using a linearized framework

Simulations of neural activity at different levels of detail are ubiquitous in modern neurosciences, aiding the interpretation of experimental data and underlying neural mechanisms at the level of cells and circuits. Extracellular measurements of brain signals reflecting transmembrane currents throughout the neural tissue remain commonplace. The lower frequencies (≲ 300Hz) of measured signals generally stem from synaptic activity driven by recurrent interactions among neural populations and computational models should also incorporate accurate predictions of such signals. Due to limited computational resources, large-scale neuronal network models (≳ 10⁶ neurons or so) often require reducing the level of biophysical detail and account mainly for times of action potentials (‘spikes’) or spike rates. Corresponding extracellular signal predictions have thus poorly accounted for their biophysical origin.

Here we propose a computational framework for predicting spatiotemporal filter kernels for such extracellular signals stemming from synaptic activity, accounting for the biophysics of neurons, populations, and recurrent connections. Signals are obtained by convolving population spike rates by appropriate kernels for each connection pathway and summing the contributions. Our main results are that kernels derived via linearized synapse and membrane dynamics, distributions of cells, conduction delay, and volume conductor model allow for accurately capturing the spatiotemporal dynamics of ground truth extracellular signals from conductance-based multicompartment neuron networks. One particular observation is that changes in the effective membrane time constants caused by persistent synapse activation must be accounted for.

The work also constitutes a major advance in computational efficiency of accurate, biophysics-based signal predictions from large-scale spike and rate-based neuron network models drastically reducing signal prediction times compared to biophysically detailed network models. This work also provides insight into how experimentally recorded low-frequency extracellular signals of neuronal activity may be approximately linearly dependent on spiking activity. A new software tool LFPykernels serves as a reference implementation of the framework.

Understanding the brain’s function and activity in healthy and pathological states across spatial scales and times spanning entire lives is one of humanity’s great undertakings. In experimental and clinical work probing the brain’s activity, a variety of electric and magnetic measurement techniques are routinely applied. However interpreting the extracellularly measured signals remains arduous due to multiple factors, mainly the large number of neurons contributing to the signals and complex interactions occurring in recurrently connected neuronal circuits. To understand how neurons give rise to such signals, mechanistic modeling combined with forward models derived using volume conductor theory has proven to be successful, but this approach currently does not scale to the systems level (encompassing millions of neurons or more) where simplified or abstract neuron representations typically are used. Motivated by experimental findings implying approximately linear relationships between times of neuronal action potentials and extracellular population signals, we provide a biophysics-based method for computing causal filters relating spikes and extracellular signals that can be applied with spike times or rates of large-scale neuronal network models for predictions of population signals without relying on ad hoc approximations.

Imbalance of flight-freeze responses and their cellular correlates in the Nlgn3-/y rat model of autism

BACKGROUND

Mutations in the postsynaptic transmembrane protein neuroligin-3 are highly correlative with autism spectrum disorders (ASDs) and intellectual disabilities (IDs). Fear learning is well studied in models of these disorders, however differences in fear response behaviours are often overlooked. We aim to examine fear behaviour and its cellular underpinnings in a rat model of ASD/ID lacking Nlgn3.

METHODS

This study uses a range of behavioural tests to understand differences in fear response behaviour in Nlgn3^-/y rats. Following this, we examined the physiological underpinnings of this in neurons of the periaqueductal grey (PAG), a midbrain area involved in flight-or-freeze responses. We used whole-cell patch-clamp recordings from ex vivo PAG slices, in addition to in vivo local-field potential recordings and electrical stimulation of the PAG in wildtype and Nlgn3^-/y rats. We analysed behavioural data with two- and three-way ANOVAS and electrophysiological data with generalised linear mixed modelling (GLMM).

RESULTS

We observed that, unlike the wildtype, Nlgn3^-/y rats are more likely to response with flight rather than freezing in threatening situations. Electrophysiological findings were in agreement with these behavioural outcomes. We found in ex vivo slices from Nlgn3^-/y rats that neurons in dorsal PAG (dPAG) showed intrinsic hyperexcitability compared to wildtype. Similarly, stimulating dPAG in vivo revealed that lower magnitudes sufficed to evoke flight behaviour in Nlgn3^-/y than wildtype rats, indicating the functional impact of the increased cellular excitability.

LIMITATIONS

Our findings do not examine what specific cell type in the PAG is likely responsible for these phenotypes. Furthermore, we have focussed on phenotypes in young adult animals, whilst the human condition associated with NLGN3 mutations appears during the first few years of life.

CONCLUSIONS

We describe altered fear responses in Nlgn3^-/y rats and provide evidence that this is the result of a circuit bias that predisposes flight over freeze responses. Additionally, we demonstrate the first link between PAG dysfunction and ASD/ID. This study provides new insight into potential pathophysiologies leading to anxiety disorders and changes to fear responses in individuals with ASD.

Phase coding of spatial representations in the human entorhinal cortex

The grid-like activity pattern of cells in the mammalian entorhinal cortex provides an internal reference frame for allocentric self-localization. The same neurons maintain robust phase couplings with local field oscillations. We found that neurons of the human entorhinal cortex display consistent spatial and temporal phase locking between spikes and slow gamma band local field potentials (LFPs) during virtual navigation. The phase locking maintained an environment-specific map over time. The phase tuning of spikes to the slow gamma band LFP revealed spatially periodic phase grids with environment-dependent scaling and consistent alignment with the environment. Using a Bayesian decoding model, we could predict the avatar's position with near perfect accuracy and, to a lesser extent, that of heading direction as well. These results imply that the phase of spikes relative to spatially modulated gamma oscillations encode allocentric spatial positions. We posit that a joint spatiotemporal phase code can implement the combined neural representation of space and time in the human entorhinal cortex.

Active Dendrites and Local Field Potentials: Biophysical Mechanisms and Computational Explorations

Neurons and glial cells are endowed with membranes that express a rich repertoire of ion channels, transporters, and receptors. The constant flux of ions across the neuronal and glial membranes results in voltage fluctuations that can be recorded from the extracellular matrix. The high frequency components of this voltage signal contain information about the spiking activity, reflecting the output from the neurons surrounding the recording location. The low frequency components of the signal, referred to as the local field potential (LFP), have been traditionally thought to provide information about the synaptic inputs that impinge on the large dendritic trees of various neurons. In this review, we discuss recent computational and experimental studies pointing to a critical role of several active dendritic mechanisms that can influence the genesis and the location-dependent spectro-temporal dynamics of LFPs, spanning different brain regions. We strongly emphasize the need to account for the several fast and slow dendritic events and associated active mechanisms - including gradients in their expression profiles, inter- and intra-cellular spatio-temporal interactions spanning neurons and glia, heterogeneities and degeneracy across scales, neuromodulatory influences, and activitydependent plasticity - towards gaining important insights about the origins of LFP under different behavioral states in health and disease. We provide simple but essential guidelines on how to model LFPs taking into account these dendritic mechanisms, with detailed methodology on how to account for various heterogeneities and electrophysiological properties of neurons and synapses while studying LFPs.

Linking minimal and detailed models of CA1 microcircuits reveals how theta rhythms emerge and their frequencies controlled

The wide variety of cell types and their biophysical complexities pose a challenge in our ability to understand oscillatory activities produced by cellular-based computational network models. This challenge stems from their high-dimensional and multiparametric natures. To overcome this, we implement a solution by linking minimal and detailed models of CA1 microcircuits that generate intrahippocampal (3-12 Hz) theta rhythms. We leverage insights from minimal models to guide explorations of more detailed models and obtain a cellular perspective of theta generation. Our findings distinguish the pyramidal cells as the theta rhythm initiators and reveal that their activity is regularized by the inhibitory cell populations, supporting a proposed hypothesis of an "inhibition-based tuning" mechanism. We find a strong correlation between input current to the pyramidal cells and the resulting local field potential theta frequency, indicating that intrinsic pyramidal cell properties underpin network frequency characteristics. This work provides a cellular-based foundation from which in vivo theta activities can be explored.

The Generation and Modulation of Distinct Gamma Oscillations with Local, Horizontal, and Feedback Connections in the Primary Visual Cortex: A Model Study on Large-Scale Networks

Gamma oscillation (GAMMA) in the local field potential (LFP) is a synchronized activity commonly found in many brain regions, and it has been thought as a functional signature of network connectivity in the brain, which plays important roles in information processing. Studies have shown that the response property of GAMMA is related to neural interaction through local recurrent connections (RC), feed-forward (FF), and feedback (FB) connections. However, the relationship between GAMMA and long-range horizontal connections (HC) in the brain remains unclear. Here, we aimed to understand this question in a large-scale network model for the primary visual cortex (V1). We created a computational model composed of multiple excitatory and inhibitory units with biologically plausible connectivity patterns for RC, FF, FB, and HC in V1; then, we quantitated GAMMA in network models at different strength levels of HC and other connection types. Surprisingly, we found that HC and FB, the two types of large-scale connections, play very different roles in generating and modulating GAMMA. While both FB and HC modulate a fast gamma oscillation (around 50-60 Hz) generated by FF and RC, HC generates a new GAMMA oscillating around 30 Hz, whose power and peak frequency can also be modulated by FB. Furthermore, response properties of the two GAMMAs in a network with both HC and FB are different in a way that is highly consistent with a recent experimental finding for distinct GAMMAs in macaque V1. The results suggest that distinct GAMMAs are signatures for neural connections in different spatial scales and they might be related to different functions for information integration. Our study, for the first time, pinpoints the underlying circuits for distinct GAMMAs in a mechanistic model for macaque V1, which might provide a new framework to study multiple gamma oscillations in other cortical regions.

Biophysically detailed forward modeling of the neural origin of EEG and MEG signals

Electroencephalography (EEG) and magnetoencephalography (MEG) are among the most important techniques for non-invasively studying cognition and disease in the human brain. These signals are known to originate from cortical neural activity, typically described in terms of current dipoles. While the link between cortical current dipoles and EEG/MEG signals is relatively well understood, surprisingly little is known about the link between different kinds of neural activity and the current dipoles themselves. Detailed biophysical modeling has played an important role in exploring the neural origin of intracranial electric signals, like extracellular spikes and local field potentials. However, this approach has not yet been taken full advantage of in the context of exploring the neural origin of the cortical current dipoles that are causing EEG/MEG signals. Here, we present a method for reducing arbitrary simulated neural activity to single current dipoles. We find that the method is applicable for calculating extracranial signals, but less suited for calculating intracranial electrocorticography (ECoG) signals. We demonstrate that this approach can serve as a powerful tool for investigating the neural origin of EEG/MEG signals. This is done through example studies of the single-neuron EEG contribution, the putative EEG contribution from calcium spikes, and from calculating EEG signals from large-scale neural network simulations. We also demonstrate how the simulated current dipoles can be used directly in combination with detailed head models, allowing for simulated EEG signals with an unprecedented level of biophysical details. In conclusion, this paper presents a framework for biophysically detailed modeling of EEG and MEG signals, which can be used to better our understanding of non-inasively measured neural activity in humans.

Modelling unitary fields and the single-neuron contribution to local field potentials in the hippocampus

Key points

We simulate the unitary local field potential (uLFP) generated in the hippocampus CA3, using morphologically detailed models.

The model suggests that cancelling effects between apical and basal dendritic synapses explain the low amplitude of excitatory uLFPs.

Inhibitory synapses around the soma do not cancel and could explain the high‐amplitude inhibitory uLFPs.

These results suggest that somatic inhibition constitutes a strong component of LFPs, which may explain a number of experimental observations.

Abstract

Synaptic currents represent a major contribution to the local field potential (LFP) in brain tissue, but the respective contribution of excitatory and inhibitory synapses is not known. Here, we provide estimates of this contribution by using computational models of hippocampal pyramidal neurons, constrained by in vitro recordings. We focus on the unitary LFP (uLFP) generated by single neurons in the CA3 region of the hippocampus. We first reproduce experimental results for hippocampal basket cells, and in particular how inhibitory uLFP are distributed within hippocampal layers. Next, we calculate the uLFP generated by pyramidal neurons, using morphologically reconstructed CA3 pyramidal cells. The model shows that the excitatory uLFP is of small amplitude, smaller than inhibitory uLFPs. Indeed, when the two are simulated together, inhibitory uLFPs mask excitatory uLFPs, which might create the illusion that the inhibitory field is generated by pyramidal cells. These results provide an explanation for the observation that excitatory and inhibitory uLFPs are of the same polarity, in vivo and in vitro. These results suggest that somatic inhibitory currents are large contributors to the LFP, which is important information for interpreting this signal. Finally, the results of our model might form the basis of a simple method to compute the LFP, which could be applied to point neurons for each cell type, thus providing a simple biologically grounded method for calculating LFPs from neural networks.

In conclusion, computational models constrained by in vitro recordings suggest that: (1) Excitatory uLFPs are of smaller amplitude than inhibitory uLFPs. (2) Inhibitory uLFPs form the major contribution to LFPs. (3) uLFPs can be used as a simple model to generate LFPs from spiking networks.

We simulate the unitary local field potential (uLFP) generated in the hippocampus CA3, using morphologically detailed models.

The model suggests that cancelling effects between apical and basal dendritic synapses explain the low amplitude of excitatory uLFPs.

Inhibitory synapses around the soma do not cancel and could explain the high‐amplitude inhibitory uLFPs.

These results suggest that somatic inhibition constitutes a strong component of LFPs, which may explain a number of experimental observations.

A Model of Memory Linking Time to Space

The storage of temporally precise spike patterns can be realized by a single neuron. A spiking neural network (SNN) model is utilized to demonstrate the ability to precisely recall a spike pattern after presenting a single input. We show by using a simulation study that the temporal properties of input patterns can be transformed into spatial patterns of local dendritic spikes. The localization of time-points of spikes is facilitated by phase-shift of the subthreshold membrane potential oscillations (SMO) in the dendritic branches, which modifies their excitability. In reference to the points in time of the arriving input, the dendritic spikes are triggered in different branches. To store spatially distributed patterns, two unsupervised learning mechanisms are utilized. Either synaptic weights to the branches, spatial representation of the temporal input pattern, are enhanced by spike-timing-dependent plasticity (STDP) or the oscillation power of SMOs in spiking branches is increased by dendritic spikes. For retrieval, spike bursts activate stored spatiotemporal patterns in dendritic branches, which reactivate the original somatic spike patterns. The simulation of the prototypical model demonstrates the principle, how linking time to space enables the storage of temporal features of an input. Plausibility, advantages, and some variations of the proposed model are also discussed.

Global sleep homeostasis reflects temporally and spatially integrated local cortical neuronal activity

Sleep homeostasis manifests as a relative constancy of its daily amount and intensity. Theoretical descriptions define ‘Process S’, a variable with dynamics dependent on global sleep-wake history, and reflected in electroencephalogram (EEG) slow wave activity (SWA, 0.5–4 Hz) during sleep. The notion of sleep as a local, activity-dependent process suggests that activity history must be integrated to determine the dynamics of global Process S. Here, we developed novel mathematical models of Process S based on cortical activity recorded in freely behaving mice, describing local Process S as a function of the deviation of neuronal firing rates from a locally defined set-point, independent of global sleep-wake state. Averaging locally derived Processes S and their rate parameters yielded values resembling those obtained from EEG SWA and global vigilance states. We conclude that local Process S dynamics reflects neuronal activity integrated over time, and global Process S reflects local processes integrated over space.

Degeneracy in hippocampal physiology and plasticity

Degeneracy, defined as the ability of structurally disparate elements to perform analogous function, has largely been assessed from the perspective of maintaining robustness of physiology or plasticity. How does the framework of degeneracy assimilate into an encoding system where the ability to change is an essential ingredient for storing new incoming information? Could degeneracy maintain the balance between the apparently contradictory goals of the need to change for encoding and the need to resist change towards maintaining homeostasis? In this review, we explore these fundamental questions with the mammalian hippocampus as an example encoding system. We systematically catalog lines of evidence, spanning multiple scales of analysis that point to the expression of degeneracy in hippocampal physiology and plasticity. We assess the potential of degeneracy as a framework to achieve the conjoint goals of encoding and homeostasis without cross-interferences. We postulate that biological complexity, involving interactions among the numerous parameters spanning different scales of analysis, could establish disparate routes towards accomplishing these conjoint goals. These disparate routes then provide several degrees of freedom to the encoding-homeostasis system in accomplishing its tasks in an input- and state-dependent manner. Finally, the expression of degeneracy spanning multiple scales offers an ideal reconciliation to several outstanding controversies, through the recognition that the seemingly contradictory disparate observations are merely alternate routes that the system might recruit towards accomplishment of its goals.

Single-Cell Membrane Potential Fluctuations Evince Network Scale-Freeness and Quasicriticality

What information single neurons receive about general neural circuit activity is a fundamental question for neuroscience. Somatic membrane potential (V _m) fluctuations are driven by the convergence of synaptic inputs from a diverse cross-section of upstream neurons. Furthermore, neural activity is often scale-free, implying that some measurements should be the same, whether taken at large or small scales. Together, convergence and scale-freeness support the hypothesis that single V _m recordings carry useful information about high-dimensional cortical activity. Conveniently, the theory of "critical branching networks" (one purported explanation for scale-freeness) provides testable predictions about scale-free measurements that are readily applied to V _m fluctuations. To investigate, we obtained whole-cell current-clamp recordings of pyramidal neurons in visual cortex of turtles with unknown genders. We isolated fluctuations in V _m below the firing threshold and analyzed them by adapting the definition of "neuronal avalanches" (i.e., spurts of population spiking). The V _m fluctuations which we analyzed were scale-free and consistent with critical branching. These findings recapitulated results from large-scale cortical population data obtained separately in complementary experiments using microelectrode arrays described previously (Shew et al., 2015). Simultaneously recorded single-unit local field potential did not provide a good match, demonstrating the specific utility of V _m Modeling shows that estimation of dynamical network properties from neuronal inputs is most accurate when networks are structured as critical branching networks. In conclusion, these findings extend evidence of critical phenomena while also establishing subthreshold pyramidal neuron V _m fluctuations as an informative gauge of high-dimensional cortical population activity.SIGNIFICANCE STATEMENT The relationship between membrane potential (V _m) dynamics of single neurons and population dynamics is indispensable to understanding cortical circuits. Just as important to the biophysics of computation are emergent properties such as scale-freeness, where critical branching networks offer insight. This report makes progress on both fronts by comparing statistics from single-neuron whole-cell recordings with population statistics obtained with microelectrode arrays. Not only are fluctuations of somatic V _m scale-free, they match fluctuations of population activity. Thus, our results demonstrate appropriation of the brain's own subsampling method (convergence of synaptic inputs) while extending the range of fundamental evidence for critical phenomena in neural systems from the previously observed mesoscale (fMRI, LFP, population spiking) to the microscale, namely, V _m fluctuations.

Multimodal Modeling of Neural Network Activity: Computing LFP, ECoG, EEG, and MEG Signals With LFPy 2.0

Recordings of extracellular electrical, and later also magnetic, brain signals have been the dominant technique for measuring brain activity for decades. The interpretation of such signals is however nontrivial, as the measured signals result from both local and distant neuronal activity. In volume-conductor theory the extracellular potentials can be calculated from a distance-weighted sum of contributions from transmembrane currents of neurons. Given the same transmembrane currents, the contributions to the magnetic field recorded both inside and outside the brain can also be computed. This allows for the development of computational tools implementing forward models grounded in the biophysics underlying electrical and magnetic measurement modalities. LFPy (LFPy.readthedocs.io) incorporated a well-established scheme for predicting extracellular potentials of individual neurons with arbitrary levels of biological detail. It relies on NEURON (neuron.yale.edu) to compute transmembrane currents of multicompartment neurons which is then used in combination with an electrostatic forward model. Its functionality is now extended to allow for modeling of networks of multicompartment neurons with concurrent calculations of extracellular potentials and current dipole moments. The current dipole moments are then, in combination with suitable volume-conductor head models, used to compute non-invasive measures of neuronal activity, like scalp potentials (electroencephalographic recordings; EEG) and magnetic fields outside the head (magnetoencephalographic recordings; MEG). One such built-in head model is the four-sphere head model incorporating the different electric conductivities of brain, cerebrospinal fluid, skull and scalp. We demonstrate the new functionality of the software by constructing a network of biophysically detailed multicompartment neuron models from the Neocortical Microcircuit Collaboration (NMC) Portal (bbp.epfl.ch/nmc-portal) with corresponding statistics of connections and synapses, and compute in vivo-like extracellular potentials (local field potentials, LFP; electrocorticographical signals, ECoG) and corresponding current dipole moments. From the current dipole moments we estimate corresponding EEG and MEG signals using the four-sphere head model. We also show strong scaling performance of LFPy with different numbers of message-passing interface (MPI) processes, and for different network sizes with different density of connections. The open-source software LFPy is equally suitable for execution on laptops and in parallel on high-performance computing (HPC) facilities and is publicly available on GitHub.com.

Deciphering the Contribution of Oriens-Lacunosum/Moleculare (OLM) Cells to Intrinsic θ Rhythms Using Biophysical Local Field Potential (LFP) Models

Oscillations in local field potentials (LFPs) are prevalent and contribute to brain function. An understanding of the cellular correlates and pathways affecting LFPs is needed, but many overlapping pathways in vivo make this difficult to achieve. A prevalent LFP rhythm in the hippocampus associated with memory processing and spatial navigation is the θ (3–12 Hz) oscillation. θ rhythms emerge intrinsically in an in vitro whole hippocampus preparation and this reduced preparation makes it possible to assess the contribution of different cell types to LFP generation. We focus on oriens-lacunosum/moleculare (OLM) cells as a major class of interneurons in the hippocampus. OLM cells can influence pyramidal (PYR) cells through two distinct pathways: by direct inhibition of PYR cell distal dendrites, and by indirect disinhibition of PYR cell proximal dendrites. We use previous inhibitory network models and build biophysical LFP models using volume conductor theory. We examine the effect of OLM cells to ongoing intrinsic LFP θ rhythms by directly comparing our model LFP features with experiment. We find that OLM cell inputs regulate the robustness of LFP responses without affecting their average power and that this robust response depends on coactivation of distal inhibition and basal excitation. We use our models to estimate the spatial extent of the region generating LFP θ rhythms, leading us to predict that about 22,000 PYR cells participate in intrinsic θ generation. Besides obtaining an understanding of OLM cell contributions to intrinsic LFP θ rhythms, our work can help decipher cellular correlates of in vivo LFPs.

Investigating large-scale brain dynamics using field potential recordings: analysis and interpretation

New technologies to record electrical activity from the brain on a massive scale offer tremendous opportunities for discovery. Electrical measurements of large-scale brain dynamics, termed field potentials, are especially important to understanding and treating the human brain. Here, our goal is to provide best practices on how field potential recordings (electroencephalograms, magnetoencephalograms, electrocorticograms and local field potentials) can be analyzed to identify large-scale brain dynamics, and to highlight critical issues and limitations of interpretation in current work. We focus our discussion of analyses around the broad themes of activation, correlation, communication and coding. We provide recommendations for interpreting the data using forward and inverse models. The forward model describes how field potentials are generated by the activity of populations of neurons. The inverse model describes how to infer the activity of populations of neurons from field potential recordings. A recurring theme is the challenge of understanding how field potentials reflect neuronal population activity given the complexity of the underlying brain systems.

Contribution of the Axon Initial Segment to Action Potentials Recorded Extracellularly

Action potentials (APs) are electric phenomena that are recorded both intracellularly and extracellularly. APs are usually initiated in the short segment of the axon called the axon initial segment (AIS). It was recently proposed that at the onset of an AP the soma and the AIS form a dipole. We study the extracellular signature [the extracellular AP (EAP)] generated by such a dipole. First, we demonstrate the formation of the dipole and its extracellular signature in detailed morphological models of a reconstructed pyramidal neuron. Then, we study the EAP waveform and its spatial dependence in models with axonal AP initiation and contrast it with the EAP obtained in models with somatic AP initiation. We show that in the models with axonal AP initiation the dipole forms between somatodendritic compartments and the AIS, and not between soma and dendrites as in the classical models. The soma-dendrites dipole is present only in models with somatic AP initiation. Our study has consequences for interpreting extracellular recordings of single-neuron activity and determining electrophysiological neuron types, but also for better understanding the origins of the high-frequency macroscopic extracellular potentials recorded in the brain.

h-Type Membrane Current Shapes the Local Field Potential from Populations of Pyramidal Neurons

In cortex, the local field potential (LFP) is thought to mainly stem from correlated synaptic input to populations of geometrically aligned neurons. Computer models of single cortical pyramidal neurons showed that subthreshold voltage-dependent membrane conductances can also shape the LFP signal, in particular the hyperpolarization-activated cation current (I_h; h-type). This ion channel is prominent in various types of pyramidal neurons, typically showing an increasing density gradient along the apical dendrites. Here, we investigate how I_h affects the LFP generated by a model of a population of cortical pyramidal neurons. We find that the LFP from populations of neurons that receive uncorrelated synaptic input can be well predicted by the LFP from single neurons. In this case, when input impinges on the distal dendrites, where most h-type channels are located, a strong resonance in the LFP was measured near the soma, whereas the opposite configuration does not reveal an I_h contribution to the LFP. Introducing correlations in the synaptic inputs to the pyramidal cells strongly amplifies the LFP, while maintaining the differential effects of I_h for distal dendritic versus perisomatic input. Previous theoretical work showed that input correlations do not amplify LFP power when neurons receive synaptic input uniformly across the cell. We find that this crucially depends on the membrane conductance distribution: the asymmetric distribution of I_h results in a strong amplification of the LFP when synaptic inputs to the cell population are correlated. In conclusion, we find that the h-type current is particularly suited to shape the LFP signal in cortical populations.SIGNIFICANCE STATEMENT The local field potential (LFP), the low-frequency part of extracellular potentials recorded in neural tissue, is often used for probing neural circuit activity. While the cortical LFP is thought to mainly reflect synaptic inputs onto pyramidal neurons, little is known about the role of subthreshold active conductances in shaping the LFP. By means of biophysical modeling we obtain a comprehensive, qualitative understanding of how LFPs generated by populations of cortical pyramidal neurons depend on active subthreshold currents, and identify the key importance of the h-type channel. Our results show that LFPs can give information about the active properties of neurons and that preferred frequencies in the LFP can result from those cellular properties instead of, for example, network dynamics.

Differential polarization of cortical pyramidal neuron dendrites through weak extracellular fields

The rise of transcranial current stimulation (tCS) techniques have sparked an increasing interest in the effects of weak extracellular electric fields on neural activity. These fields modulate ongoing neural activity through polarization of the neuronal membrane. While the somatic polarization has been investigated experimentally, the frequency-dependent polarization of the dendritic trees in the presence of alternating (AC) fields has received little attention yet. Using a biophysically detailed model with experimentally constrained active conductances, we analyze the subthreshold response of cortical pyramidal cells to weak AC fields, as induced during tCS. We observe a strong frequency resonance around 10-20 Hz in the apical dendrites sensitivity to polarize in response to electric fields but not in the basal dendrites nor the soma. To disentangle the relative roles of the cell morphology and active and passive membrane properties in this resonance, we perform a thorough analysis using simplified models, e.g. a passive pyramidal neuron model, simple passive cables and reconstructed cell model with simplified ion channels. We attribute the origin of the resonance in the apical dendrites to (i) a locally increased sensitivity due to the morphology and to (ii) the high density of h-type channels. Our systematic study provides an improved understanding of the subthreshold response of cortical cells to weak electric fields and, importantly, allows for an improved design of tCS stimuli.

An Interneuron Circuit Reproducing Essential Spectral Features of Field Potentials

Recent advances in engineering and signal processing have renewed the interest in invasive and surface brain recordings, yet many features of cortical field potentials remain incompletely understood. In the computational study that follows, we show that a model circuit of interneurons, coupled via both GABA_A receptor synapses and electrical synapses, reproduces many essential features of the power spectrum of local field potential (LFP) recordings, such as 1/ f power scaling at low frequency (below 10 Hz), power accumulation in the γ-frequency band (30-100 Hz), and a robust α rhythm in the absence of stimulation. The low-frequency 1/ f power scaling depends on strong reciprocal inhibition, whereas the α rhythm is generated by electrical coupling of intrinsically active neurons. As in previous studies, the γ power arises through the amplification of single-neuron spectral properties, owing to the refractory period, by parameters that favor neuronal synchrony, such as delayed inhibition. This study also confirms that both synaptic and voltage-gated membrane currents contribute substantially to the LFP and that high-frequency signals such as action potentials quickly taper off with distance. Given the ubiquity of electrically coupled interneuron circuits in the mammalian brain, they may be major determinants of the recorded potentials.

Synaptic integrative mechanisms for spatial cognition

Synaptic integrative mechanisms have profound effects on electrical signaling in the brain that, although largely hidden from recording methods that observe the spiking activity of neurons, may be critical for the encoding, storage and retrieval of information. Here we review roles for synaptic integrative mechanisms in the selection, generation and plasticity of place and grid fields, and in related temporal codes for the representation of space. We outline outstanding questions and challenges in the testing of hypothesized models for spatial computation and memory.

Correlated Disruption of Resting-State fMRI, LFP, and Spike Connectivity between Area 3b and S2 following Spinal Cord Injury in Monkeys

This study aims to understand how functional connectivity (FC) between areas 3b and S2 alters following input deprivation and the neuronal basis of disrupted FC of resting-state fMRI signals. We combined submillimeter fMRI with microelectrode recordings to localize the deafferented digit regions in areas 3b and S2 by mapping tactile stimulus-evoked fMRI activations before and after cervical dorsal column lesion in each male monkey. An average afferent disruption of 97% significantly reduced fMRI, local field potential (LFP), and spike responses to stimuli in both areas. Analysis of resting-state fMRI signal correlation, LFP coherence, and spike cross-correlation revealed significantly reduced functional connectivity between deafferented areas 3b and S2. The degrees of reductions in stimulus responsiveness and FC after deafferentation differed across fMRI, LFP, and spiking signals. The reduction of FC was much weaker than that of stimulus-evoked responses. Whereas the largest stimulus-evoked signal drop (∼80%) was observed in LFP signals, the greatest FC reduction was detected in the spiking activity (∼30%). fMRI signals showed mild reductions in stimulus responsiveness (∼25%) and FC (∼20%). The overall deafferentation-induced changes were quite similar in areas 3b and S2 across signals. Here we demonstrated that FC strength between areas 3b and S2 was much weakened by dorsal column lesion, and stimulus response reduction and FC disruption in fMRI covary with those of LFP and spiking signals in deafferented areas 3b and S2. These findings have important implications for fMRI studies aiming to probe FC alterations in pathological conditions involving deafferentation in humans.SIGNIFICANCE STATEMENT By directly comparing fMRI, local field potential, and spike signals in both tactile stimulation and resting states before and after severe disruption of dorsal column afferent, we demonstrated that reduction in fMRI responses to stimuli is accompanied by weakened resting-state fMRI functional connectivity (FC) in input-deprived and reorganized digit regions in area 3b of the S1 and S2. Concurrent reductions in local field potential and spike FC validated the use of resting-state fMRI signals for probing neural intrinsic FC alterations in pathological deafferented cortex, and indicated that disrupted FC between mesoscale functionally highly related regions may contribute to the behavioral impairments.

Signatures of Somatic Inhibition and Dendritic Excitation in Auditory Brainstem Field Potentials

Extracellular voltage recordings (V_e ; field potentials) provide an accessible view of in vivo neural activity, but proper interpretation of field potentials is a long-standing challenge. Computational modeling can aid in identifying neural generators of field potentials. In the auditory brainstem of cats, spatial patterns of sound-evoked V_e can resemble, strikingly, V_e generated by current dipoles. Previously, we developed a biophysically-based model of a binaural brainstem nucleus, the medial superior olive (MSO), that accounts qualitatively for observed dipole-like V_e patterns in sustained responses to monaural tones with frequencies >∼1000 Hz (Goldwyn et al., 2014). We have observed, however, that V_e patterns in cats of both sexes appear more monopole-like for lower-frequency tones. Here, we enhance our theory to accurately reproduce dipole and non-dipole features of V_e responses to monaural tones with frequencies ranging from 600 to 1800 Hz. By applying our model to data, we estimate time courses of paired input currents to MSO neurons. We interpret these inputs as dendrite-targeting excitation and soma-targeting inhibition (the latter contributes non-dipole-like features to V_e responses). Aspects of inferred inputs are consistent with synaptic inputs to MSO neurons including the tendencies of inhibitory inputs to attenuate in response to high-frequency tones and to precede excitatory inputs. Importantly, our updated theory can be tested experimentally by blocking synaptic inputs. MSO neurons perform a critical role in sound localization and binaural hearing. By solving an inverse problem to uncover synaptic inputs from V_e patterns we provide a new perspective on MSO physiology.SIGNIFICANCE STATEMENT Extracellular voltages (field potentials) are a common measure of brain activity. Ideally, one could infer from these data the activity of neurons and synapses that generate field potentials, but this "inverse problem" is not easily solved. We study brainstem field potentials in the region of the medial superior olive (MSO); a critical center in the auditory pathway. These field potentials exhibit distinctive spatial and temporal patterns in response to pure tone sounds. We use mathematical modeling in combination with physiological and anatomical knowledge of MSO neurons to plausibly explain how dendrite-targeting excitation and soma-targeting inhibition generate these field potentials. Inferring putative synaptic currents from field potentials advances our ability to study neural processing of sound in the MSO.

Combining Theory, Model, and Experiment to Explain How Intrinsic Theta Rhythms Are Generated in an In Vitro Whole Hippocampus Preparation without Oscillatory Inputs

Scientists have observed local field potential theta rhythms (3-12 Hz) in the hippocampus for decades, but understanding the mechanisms underlying their generation is complicated by their diversity in pharmacological and frequency profiles. In addition, interactions with other brain structures and oscillatory drives to the hippocampus during distinct brain states has made it difficult to identify hippocampus-specific properties directly involved in theta generation. To overcome this, we develop cellular-based network models using a whole hippocampus in vitro preparation that spontaneously generates theta rhythms. Building on theoretical and computational analyses, we find that spike frequency adaptation and postinhibitory rebound constitute a basis for theta generation in large, minimally connected CA1 pyramidal (PYR) cell network models with fast-firing parvalbumin-positive (PV⁺) inhibitory cells. Sparse firing of PYR cells and large excitatory currents onto PV⁺ cells are present as in experiments. The particular theta frequency is more controlled by PYR-to-PV⁺ cell interactions rather than PV⁺-to-PYR cell interactions. We identify two scenarios by which theta rhythms can emerge, and they can be differentiated by the ratio of excitatory to inhibitory currents to PV⁺ cells, but not to PYR cells. Only one of the scenarios is consistent with data from the whole hippocampus preparation, which leads to the prediction that the connection probability from PV⁺ to PYR cells needs to be larger than from PYR to PV⁺ cells. Our models can serve as a platform on which to build and develop an understanding of in vivo theta generation.

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).

An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons

Two mathematical models are part of the foundation of Computational neurophysiology; (a) the Cable equation is used to compute the membrane potential of neurons, and, (b) volume-conductor theory describes the extracellular potential around neurons. In the standard procedure for computing extracellular potentials, the transmembrane currents are computed by means of (a) and the extracellular potentials are computed using an explicit sum over analytical point-current source solutions as prescribed by volume conductor theory. Both models are extremely useful as they allow huge simplifications of the computational efforts involved in computing extracellular potentials. However, there are more accurate, though computationally very expensive, models available where the potentials inside and outside the neurons are computed simultaneously in a self-consistent scheme. In the present work we explore the accuracy of the classical models (a) and (b) by comparing them to these more accurate schemes. The main assumption of (a) is that the ephaptic current can be ignored in the derivation of the Cable equation. We find, however, for our examples with stylized neurons, that the ephaptic current is comparable in magnitude to other currents involved in the computations, suggesting that it may be significant-at least in parts of the simulation. The magnitude of the error introduced in the membrane potential is several millivolts, and this error also translates into errors in the predicted extracellular potentials. While the error becomes negligible if we assume the extracellular conductivity to be very large, this assumption is, unfortunately, not easy to justify a priori for all situations of interest.

Focal Local Field Potential Signature of the Single-Axon Monosynaptic Thalamocortical Connection

A resurgence has taken place in recent years in the use of the extracellularly recorded local field potential (LFP) to investigate neural network activity. To probe monosynaptic thalamic activation of cortical postsynaptic target cells, so called spike-trigger-averaged LFP (stLFP) signatures have been measured. In these experiments, the cortical LFP is measured by multielectrodes covering several cortical lamina and averaged on spontaneous spikes of thalamocortical (TC) cells. Using a well established forward-modeling scheme, we investigated the biophysical origin of this stLFP signature with simultaneous synaptic activation of cortical layer-4 neurons, mimicking the effect of a single afferent spike from a single TC neuron. Constrained by previously measured intracellular responses of the main postsynaptic target cell types and with biologically plausible assumptions regarding the spatial distribution of thalamic synaptic inputs into layer 4, the model predicted characteristic contributions to monosynaptic stLFP signatures both for the regular-spiking (RS) excitatory neurons and the fast-spiking (FS) inhibitory interneurons. In particular, the FS cells generated stLFP signatures of shorter temporal duration than the RS cells. Added together, a sum of the stLFP signatures of these two principal synaptic targets of TC cells were observed to resemble experimentally measured stLFP signatures. Outside the volume targeted by TC afferents, the resulting postsynaptic LFP signals were found to be sharply attenuated. This implies that such stLFP signatures provide a very local measure of TC synaptic activation, and that newly developed inverse current-source density (CSD)-estimation methods are needed for precise assessment of the underlying spatiotemporal CSD profiles.

SIGNIFICANCE STATEMENT Despite its long history and prevalent use, the proper interpretation of the extracellularly recorded local field potential (LFP) is still not fully established. Here we investigate by biophysical modeling the origin of the focal LFP signature of the single-axon monosynaptic thalamocortical connection as measured by spike-trigger-averaging of cortical LFPs on spontaneous spikes of thalamocortical neurons. We find that this LFP signature is well accounted for by a model assuming thalamic projections to two cortical layer-4 cell populations: one excitatory (putatively regular-spiking cells) and one inhibitory (putatively fast-spiking cells). The LFP signature is observed to decay sharply outside the cortical region receiving the thalamocortical projection, implying that it indeed provides a very local measure of thalamocortical synaptic activation.

Strings on a Violin: Location Dependence of Frequency Tuning in Active Dendrites

Strings on a violin are tuned to generate distinct sound frequencies in a manner that is firmly dependent on finger location along the fingerboard. Sound frequencies emerging from different violins could be very different based on their architecture, the nature of strings and their tuning. Analogously, active neuronal dendrites, dendrites endowed with active channel conductances, are tuned to distinct input frequencies in a manner that is dependent on the dendritic location of the synaptic inputs. Further, disparate channel expression profiles and differences in morphological characteristics could result in dendrites on different neurons of the same subtype tuned to distinct frequency ranges. Alternately, similar location-dependence along dendritic structures could be achieved through disparate combinations of channel profiles and morphological characteristics, leading to degeneracy in active dendritic spectral tuning. Akin to strings on a violin being tuned to different frequencies than those on a viola or a cello, different neuronal subtypes exhibit distinct channel profiles and disparate morphological characteristics endowing each neuronal subtype with unique location-dependent frequency selectivity. Finally, similar to the tunability of musical instruments to elicit distinct location-dependent sounds, neuronal frequency selectivity and its location-dependence are tunable through activity-dependent plasticity of ion channels and morphology. In this morceau, we explore the origins of neuronal frequency selectivity, and survey the literature on the mechanisms behind the emergence of location-dependence in distinct forms of frequency tuning. As a coda to this composition, we present some future directions for this exciting convergence of biophysical mechanisms that endow a neuron with frequency multiplexing capabilities.

Local field potentials primarily reflect inhibitory neuron activity in human and monkey cortex

The local field potential (LFP) is generated by large populations of neurons, but unitary contribution of spiking neurons to LFP is not well characterised. We investigated this contribution in multi-electrode array recordings from human and monkey neocortex by examining the spike-triggered LFP average (st-LFP). The resulting st-LFPs were dominated by broad spatio-temporal components due to ongoing activity, synaptic inputs and recurrent connectivity. To reduce the spatial reach of the st-LFP and observe the local field related to a single spike we applied a spatial filter, whose weights were adapted to the covariance of ongoing LFP. The filtered st-LFPs were limited to the perimeter of 800 μm around the neuron, and propagated at axonal speed, which is consistent with their unitary nature. In addition, we discriminated between putative inhibitory and excitatory neurons and found that the inhibitory st-LFP peaked at shorter latencies, consistently with previous findings in hippocampal slices. Thus, in human and monkey neocortex, the LFP reflects primarily inhibitory neuron activity.

Dipolar extracellular potentials generated by axonal projections

Extracellular field potentials (EFPs) are an important source of information in neuroscience, but their physiological basis is in many cases still a matter of debate. Axonal sources are typically discounted in modeling and data analysis because their contributions are assumed to be negligible. Here, we established experimentally and theoretically that contributions of axons to EFPs can be significant. Modeling action potentials propagating along axons, we showed that EFPs were prominent in the presence of terminal zones where axons branch and terminate in close succession, as found in many brain regions. Our models predicted a dipolar far field and a polarity reversal at the center of the terminal zone. We confirmed these predictions using EFPs from the barn owl auditory brainstem where we recorded in nucleus laminaris using a multielectrode array. These results demonstrate that axonal terminal zones can produce EFPs with considerable amplitude and spatial reach.

Impedance Spectrum in Cortical Tissue: Implications for Propagation of LFP Signals on the Microscopic Level

Brain research investigating electrical activity within neural tissue is producing an increasing amount of physiological data including local field potentials (LFPs) obtained via extracellular in vivo and in vitro recordings. In order to correctly interpret such electrophysiological data, it is vital to adequately understand the electrical properties of neural tissue itself. An ongoing controversy in the field of neuroscience is whether such frequency-dependent effects bias LFP recordings and affect the proper interpretation of the signal. On macroscopic scales and with large injected currents, previous studies have found various grades of frequency dependence of cortical tissue, ranging from negligible to strong, within the frequency band typically considered relevant for neuroscience (less than a few thousand hertz). Here, we performed a detailed investigation of the frequency dependence of the conductivity within cortical tissue at microscopic distances using small current amplitudes within the typical (neuro)physiological micrometer and sub-nanoampere range. We investigated the propagation of LFPs, induced by extracellular electrical current injections via patch-pipettes, in acute rat brain slice preparations containing the somatosensory cortex in vitro using multielectrode arrays. Based on our data, we determined the cortical tissue conductivity over a 100-fold increase in signal frequency (5-500 Hz). Our results imply at most very weak frequency-dependent effects within the frequency range of physiological LFPs. Using biophysical modeling, we estimated the impact of different putative impedance spectra. Our results indicate that frequency dependencies of the order measured here and in most other studies have negligible impact on the typical analysis and modeling of LFP signals from extracellular brain recordings.

Assessing human brain impedance using simultaneous surface and intracerebral recordings

Most of the literature on the brain impedance proposes a frequency-independent resistive model. Recently, this conclusion was tackled by a series of papers (Bédard et al., 2006; Bédard and Destexhe, 2009; Gomes et al., 2016), based on microscopic sale modeling and measurements. Our paper aims to investigate the impedance issue using simultaneous in vivo depth and surface signals recorded during intracerebral electrical stimulation of epileptic patients, involving a priori different tissues with different impedances. Our results confirm the conclusions from Logothethis et al. (2007): there is no evidence of frequency dependence of the brain tissue impedance (more precisely, there is no difference, in terms of frequency filtering, between the brain and the skull bone), at least at a macroscopic scale. In order to conciliate findings from both microscopic and macroscopic scales, we recall different neural/synaptic current generators' models from the literature and we propose an original computational model, based on fractional dynamics.

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems. This assumption remains to be verified. We here present a hybrid simulation framework that accounts for diffusive effects on the ECS potential. The framework uses (1) the NEURON simulator to compute the activity and ionic output currents from multicompartmental neuron models, and (2) the electrodiffusive Kirchhoff-Nernst-Planck framework to simulate the resulting dynamics of the potential and ion concentrations in the ECS, accounting for the effect of electrical migration as well as diffusion. Using this framework, we explore the effect that ECS diffusion has on the electrical potential surrounding a small population of 10 pyramidal neurons. The neural model was tuned so that simulations over ∼100 seconds of biological time led to shifts in ECS concentrations by a few millimolars, similar to what has been seen in experiments. By comparing simulations where ECS diffusion was absent with simulations where ECS diffusion was included, we made the following key findings: (i) ECS diffusion shifted the local potential by up to ∼0.2 mV. (ii) The power spectral density (PSD) of the diffusion-evoked potential shifts followed a 1/f2 power law. (iii) Diffusion effects dominated the PSD of the ECS potential for frequencies up to several hertz. In scenarios with large, but physiologically realistic ECS concentration gradients, diffusion was thus found to affect the ECS potential well within the frequency range picked up in experimental recordings.

Hybrid Scheme for Modeling Local Field Potentials from Point-Neuron Networks

With rapidly advancing multi-electrode recording technology, the local field potential (LFP) has again become a popular measure of neuronal activity in both research and clinical applications. Proper understanding of the LFP requires detailed mathematical modeling incorporating the anatomical and electrophysiological features of neurons near the recording electrode, as well as synaptic inputs from the entire network. Here we propose a hybrid modeling scheme combining efficient point-neuron network models with biophysical principles underlying LFP generation by real neurons. The LFP predictions rely on populations of network-equivalent multicompartment neuron models with layer-specific synaptic connectivity, can be used with an arbitrary number of point-neuron network populations, and allows for a full separation of simulated network dynamics and LFPs. We apply the scheme to a full-scale cortical network model for a ∼1 mm² patch of primary visual cortex, predict laminar LFPs for different network states, assess the relative LFP contribution from different laminar populations, and investigate effects of input correlations and neuron density on the LFP. The generic nature of the hybrid scheme and its public implementation in hybridLFPy form the basis for LFP predictions from other and larger point-neuron network models, as well as extensions of the current application with additional biological detail.