Inhibitory networks of fast-spiking interneurons generate slow population activities due to excitatory fluctuations and network multistability

Site-dependent shaping of field potential waveforms

The activity of neuron populations gives rise to field potentials (FPs) that extend beyond the sources. Their mixing in the volume dilutes the original temporal motifs in a site-dependent manner, a fact that has received little attention. And yet, it potentially rids of physiological significance the time-frequency parameters of individual waves (amplitude, phase, duration). This is most likely to happen when a single source or a local origin is erroneously assumed. Recent studies using spatial treatment of these signals and anatomically realistic modeling of neuron aggregates provide convincing evidence for the multisource origin and site-dependent blend of FPs. Thus, FPs generated in primary structures like the neocortex and hippocampus reach far and cross-contaminate each other but also, they add and even impose their temporal traits on distant regions. Furthermore, both structures house neurons that act as spatially distinct (but overlapped) FP sources whose activation is state, region, and time dependent, making the composition of so-called local FPs highly volatile and strongly site dependent. Since the spatial reach cannot be predicted without source geometry, it is important to assess whether waveforms and temporal motifs arise from a single source; otherwise, those from each of the co-active sources should be sought.

Inhibitory Network Bistability Explains Increased Interneuronal Activity Prior to Seizure Onset

Recent experimental literature has revealed that GABAergic interneurons exhibit increased activity prior to seizure onset, alongside additional evidence that such activity is synchronous and may arise abruptly. These findings have led some to hypothesize that this interneuronal activity may serve a causal role in driving the sudden change in brain activity that heralds seizure onset. However, the mechanisms predisposing an inhibitory network toward increased activity, specifically prior to ictogenesis, without a permanent change to inputs to the system remain unknown. We address this question by comparing simulated inhibitory networks containing control interneurons and networks containing hyperexcitable interneurons modeled to mimic treatment with 4-Aminopyridine (4-AP), an agent commonly used to model seizures in vivo and in vitro. Our in silico study demonstrates that model inhibitory networks with 4-AP interneurons are more prone than their control counterparts to exist in a bistable state in which asynchronously firing networks can abruptly transition into synchrony driven by a brief perturbation. This transition into synchrony brings about a corresponding increase in overall firing rate. We further show that perturbations driving this transition could arise in vivo from background excitatory synaptic activity in the cortex. Thus, we propose that bistability explains the increase in interneuron activity observed experimentally prior to seizure via a transition from incoherent to coherent dynamics. Moreover, bistability explains why inhibitory networks containing hyperexcitable interneurons are more vulnerable to this change in dynamics, and how such networks can undergo a transition without a permanent change in the drive. We note that while our comparisons are between networks of control and ictogenic neurons, the conclusions drawn specifically relate to the unusual dynamics that arise prior to seizure, and not seizure onset itself. However, providing a mechanistic explanation for this phenomenon specifically in a pro-ictogenic setting generates experimentally testable hypotheses regarding the role of inhibitory neurons in pre-ictal neural dynamics, and motivates further computational research into mechanisms underlying a newly hypothesized multi-step pathway to seizure initiated by inhibition.

Nanodiamonds-induced effects on neuronal firing of mouse hippocampal microcircuits

Fluorescent nanodiamonds (FND) are carbon-based nanomaterials that can efficiently incorporate optically active photoluminescent centers such as the nitrogen-vacancy complex, thus making them promising candidates as optical biolabels and drug-delivery agents. FNDs exhibit bright fluorescence without photobleaching combined with high uptake rate and low cytotoxicity. Focusing on FNDs interference with neuronal function, here we examined their effect on cultured hippocampal neurons, monitoring the whole network development as well as the electrophysiological properties of single neurons. We observed that FNDs drastically decreased the frequency of inhibitory (from 1.81 Hz to 0.86 Hz) and excitatory (from 1.61 to 0.68 Hz) miniature postsynaptic currents, and consistently reduced action potential (AP) firing frequency (by 36%), as measured by microelectrode arrays. On the contrary, bursts synchronization was preserved, as well as the amplitude of spontaneous inhibitory and excitatory events. Current-clamp recordings revealed that the ratio of neurons responding with AP trains of high-frequency (fast-spiking) versus neurons responding with trains of low-frequency (slow-spiking) was unaltered, suggesting that FNDs exerted a comparable action on neuronal subpopulations. At the single cell level, rapid onset of the somatic AP (“kink”) was drastically reduced in FND-treated neurons, suggesting a reduced contribution of axonal and dendritic components while preserving neuronal excitability.

Feedback Inhibition Shapes Emergent Computational Properties of Cortical Microcircuit Motifs

Cortical microcircuits are very complex networks, but they are composed of a relatively small number of stereotypical motifs. Hence, one strategy for throwing light on the computational function of cortical microcircuits is to analyze emergent computational properties of these stereotypical microcircuit motifs. We are addressing here the question how spike timing-dependent plasticity shapes the computational properties of one motif that has frequently been studied experimentally: interconnected populations of pyramidal cells and parvalbumin-positive inhibitory cells in layer 2/3. Experimental studies suggest that these inhibitory neurons exert some form of divisive inhibition on the pyramidal cells. We show that this data-based form of feedback inhibition, which is softer than that of winner-take-all models that are commonly considered in theoretical analyses, contributes to the emergence of an important computational function through spike timing-dependent plasticity: The capability to disentangle superimposed firing patterns in upstream networks, and to represent their information content through a sparse assembly code.SIGNIFICANCE STATEMENT We analyze emergent computational properties of a ubiquitous cortical microcircuit motif: populations of pyramidal cells that are densely interconnected with inhibitory neurons. Simulations of this model predict that sparse assembly codes emerge in this microcircuit motif under spike timing-dependent plasticity. Furthermore, we show that different assemblies will represent different hidden sources of upstream firing activity. Hence, we propose that spike timing-dependent plasticity enables this microcircuit motif to perform a fundamental computational operation on neural activity patterns.

Interaction between synaptic inhibition and glial-potassium dynamics leads to diverse seizure transition modes in biophysical models of human focal seizures

How focal seizures initiate and evolve in human neocortex remains a fundamental problem in neuroscience. Here, we use biophysical neuronal network models of neocortical patches to study how the interaction between inhibition and extracellular potassium ([K (+)] o ) dynamics may contribute to different types of focal seizures. Three main types of propagated focal seizures observed in recent intracortical microelectrode recordings in humans were modelled: seizures characterized by sustained (∼30-60 Hz) gamma local field potential (LFP) oscillations; seizures where the onset in the propagated site consisted of LFP spikes that later evolved into rhythmic (∼2-3 Hz) spike-wave complexes (SWCs); and seizures where a brief stage of low-amplitude fast-oscillation (∼10-20 Hz) LFPs preceded the SWC activity. Our findings are fourfold: (1) The interaction between elevated [K (+)] o (due to abnormal potassium buffering by glial cells) and the strength of synaptic inhibition plays a predominant role in shaping these three types of seizures. (2) Strengthening of inhibition leads to the onset of sustained narrowband gamma seizures. (3) Transition into SWC seizures is obtained either by the weakening of inhibitory synapses, or by a transient strengthening followed by an inhibitory breakdown (e.g. GABA depletion). This reduction or breakdown of inhibition among fast-spiking (FS) inhibitory interneurons increases their spiking activity and leads them eventually into depolarization block. Ictal spike-wave discharges in the model are then sustained solely by pyramidal neurons. (4) FS cell dynamics are also critical for seizures where the evolution into SWC activity is preceded by low-amplitude fast oscillations. Different levels of elevated [K (+)] o were important for transitions into and maintenance of sustained gamma oscillations and SWC discharges. Overall, our modelling study predicts that the interaction between inhibitory interneurons and [K (+)] o glial buffering under abnormal conditions may explain different types of ictal transitions and dynamics during propagated seizures in human focal epilepsy.

Regulation of Irregular Neuronal Firing by Autaptic Transmission

The importance of self-feedback autaptic transmission in modulating spike-time irregularity is still poorly understood. By using a biophysical model that incorporates autaptic coupling, we here show that self-innervation of neurons participates in the modulation of irregular neuronal firing, primarily by regulating the occurrence frequency of burst firing. In particular, we find that both excitatory and electrical autapses increase the occurrence of burst firing, thus reducing neuronal firing regularity. In contrast, inhibitory autapses suppress burst firing and therefore tend to improve the regularity of neuronal firing. Importantly, we show that these findings are independent of the firing properties of individual neurons, and as such can be observed for neurons operating in different modes. Our results provide an insightful mechanistic understanding of how different types of autapses shape irregular firing at the single-neuron level, and they highlight the functional importance of autaptic self-innervation in taming and modulating neurodynamics.

New uses of LFPs: Pathway-specific threads obtained through spatial discrimination

Local field potentials (LFPs) reflect the coordinated firing of functional neural assemblies during information coding and transfer across neural networks. As such, it was proposed that the extraordinary variety of cytoarchitectonic elements in the brain is responsible for the wide range of amplitudes and for the coverage of field potentials, which in most cases receive contributions from multiple pathways and populations. The influence of spatial factors overrides the bold interpretations of customary measurements, such as the amplitude and polarity, to the point that their cellular interpretation is one of the hardest tasks in Neurophysiology. Temporal patterns and frequency bands are not exclusive to pathways but rather, the spatial configuration of the voltage gradients created by each pathway is highly specific and may be used advantageously. Recent technical and analytical advances now make it possible to separate and then reconstruct activity for specific pathways. In this review, we discuss how spatial features specific to cells and populations define the amplitude and extension of LFPs, why they become virtually indecipherable when several pathways are co-activated, and then we present the recent advances regarding their disentanglement using spatial discrimination techniques. The pathway-specific threads of LFPs have a simple cellular interpretation, and the temporal fluctuations obtained can be applied to a variety of new experimental objectives and improve existing approaches. Among others, they facilitate the parallel readout of activity in several populations over multiple time scales correlating them with behavior. Also, they access information contained in irregular fluctuations, facilitating the testing of ongoing plasticity. In addition, they open the way to unravel the synaptic nature of rhythmic oscillations, as well as the dynamic relationships between multiple oscillatory activities. The challenge of understanding which waves belong to which populations, and the pathways that provoke them, may soon be overcome.

Diversity of LFPs Activated in Different Target Regions by a Common CA3 Input

Identifying the pathways contributing to local field potential (LFP) events and oscillations is essential to determine whether synchronous interregional patterns indicate functional connectivity. Here, we studied experimentally and numerically how different target structures receiving input from a common population shape their LFPs. We focused on the bilateral CA3 that sends gamma-paced excitatory packages to the bilateral CA1, the lateral septum, and itself (recurrent input). The CA3-specific contribution was isolated from multisite LFPs in target regions using spatial discrimination techniques. We found strong modulation of LFPs by target-specific features, including the morphology and population arrangement of cells, the timing of CA3 inputs, volume conduction from nearby targets, and co-activated inhibition. Jointly they greatly affect the LFP amplitude, profile, and frequency characteristics. For instance, ipsilateral (Schaffer) LFPs occluded contralateral ones, and septal LFPs arise mostly from remote sources while local contribution from CA3 input was minor. In the CA3 itself, gamma waves have dual origin from local networks: in-phase excitatory and nearly antiphase inhibitory. Also, waves may have different duration and varying phase in different targets. These results indicate that to explore the cellular basis of LFPs and the functional connectivity between structures, besides identifying the origin population/s, target modifiers should be considered.

Intracellular activities related to in vitro hippocampal sharp waves are altered in CA3 pyramidal neurons of aged mice

Pyramidal neurons in the hippocampal CA3 area interconnect intensively via recurrent axonal collaterals, and such CA3-to-CA3 recurrent circuitry plays important roles in the generation of hippocampal network activities. In particular, the CA3 circuitry is able to generate spontaneous sharp waves (SPWs) when examined in vitro. These in vitro SPWs are thought to result from the network activity of GABAergic inhibitory interneurons as SPW-correlating intracellular activities are featured with strong IPSPs in pyramidal neurons and EPSPs or spikes in GABAergic interneurons. In view of accumulating evidence indicating a decrease in subgroups of hippocampal GABAergic interneurons in aged animals, we test the hypothesis that the intracellular activities related to in vitro SPWs are altered in CA3 pyramidal neurons of aged mice. Hippocampal slices were prepared from adult and aged C57 black mice (ages 3-6 and 24-28months respectively). Population and single-cell activities were examined via extracellular and whole-cell patch-clamp recordings. CA3 SPW frequencies were not significantly different between the slices of adult and aged mice but SPW-correlating intracellular activities featured weaker IPSC components in aged CA3 pyramidal neurons compared to adult neurons. It was unlikely that this latter phenomenon was due to general impairments of GABAergic synapses in the aged CA3 circuitry as evoked IPSC responses and pharmacologically isolated IPSCs were observed in aged CA3 pyramidal neurons. In addition, aged CA3 pyramidal neurons displayed more positive resting potentials and had a higher propensity of burst firing than adult neurons. We postulate that alterations of GABAergic network activity may explain the reduced IPCS contributions to in vitro SPWs in aged CA3 pyramidal neurons. Overall, our present observations are supportive of the notion that excitability of hippocampal CA3 circuitry is increased in aged mice.

Simple, biologically-constrained CA1 pyramidal cell models using an intact, whole hippocampus context

The hippocampus is a heavily studied brain structure due to its involvement in learning and memory. Detailed models of excitatory, pyramidal cells in hippocampus have been developed using a range of experimental data. These models have been used to help us understand, for example, the effects of synaptic integration and voltage gated channel densities and distributions on cellular responses. However, these cellular outputs need to be considered from the perspective of the networks in which they are embedded. Using modeling approaches, if cellular representations are too detailed, it quickly becomes computationally unwieldy to explore large network simulations. Thus, simple models are preferable, but at the same time they need to have a clear, experimental basis so as to allow physiologically based understandings to emerge. In this article, we describe the development of simple models of CA1 pyramidal cells, as derived in a well-defined experimental context of an intact, whole hippocampus preparation expressing population oscillations. These models are based on the intrinsic properties and frequency-current profiles of CA1 pyramidal cells, and can be used to build, fully examine, and analyze large networks.

Scale-free brain activity: past, present, and future

Brain activity observed at many spatiotemporal scales exhibits a 1/f-like power spectrum, including neuronal membrane potentials, neural field potentials, noninvasive electroencephalography (EEG), magnetoencephalography (MEG), and functional magnetic resonance imaging (fMRI) signals. A 1/f-like power spectrum is indicative of arrhythmic brain activity that does not contain a predominant temporal scale (hence, 'scale-free'). This characteristic of scale-free brain activity distinguishes it from brain oscillations. Although scale-free brain activity and brain oscillations coexist, our understanding of the former remains limited. Recent research has shed light on the spatiotemporal organization, functional significance, and potential generative mechanisms of scale-free brain activity, as well as its developmental and clinical relevance. A deeper understanding of this prevalent brain signal should provide new insights into, and analytical tools for, cognitive neuroscience.

Network models predict that reduced excitatory fluctuations can give rise to hippocampal network hyper-excitability in MeCP2-null mice

Rett syndrome is a severe pediatric neurological disorder caused by loss of function mutations within the gene encoding methyl CpG-binding protein 2 (MeCP2). Although MeCP2 is expressed near ubiquitously, the primary pathophysiology of Rett syndrome stems from impairments of nervous system function. One alteration within different regions of the MeCP2-deficient brain is the presence of hyper-excitable network responses. In the hippocampus, such responses exist despite there being an overall decrease in spontaneous excitatory drive within the network. In this study, we generated and used mathematical, neuronal network models to resolve this apparent paradox. We did this by taking advantage of previous mathematical modelling insights that indicated that decreased excitatory fluctuations, but not mean excitatory drive, more critically explain observed changes in hippocampal network oscillations from MeCP2-null mouse slices. Importantly, reduced excitatory fluctuations could also bring about hyper-excitable responses in our network models. Therefore, these results indicate that diminished excitatory fluctuations may be responsible for the hyper-excitable state of MeCP2-deficient hippocampal circuitry.

Modeling oscillatory dynamics in brain microcircuits as a way to help uncover neurological disease mechanisms: a proposal

There is an undisputed need and requirement for theoretical and computational studies in Neuroscience today. Furthermore, it is clear that oscillatory dynamical output from brain networks is representative of various behavioural states, and it is becoming clear that one could consider these outputs as measures of normal and pathological brain states. Although mathematical modeling of oscillatory dynamics in the context of neurological disease exists, it is a highly challenging endeavour because of the many levels of organization in the nervous system. This challenge is coupled with the increasing knowledge of cellular specificity and network dysfunction that is associated with disease. Recently, whole hippocampus in vitro preparations from control animals have been shown to spontaneously express oscillatory activities. In addition, when using preparations derived from animal models of disease, these activities show particular alterations. These preparations present an opportunity to address challenges involved with using models to gain insight because of easier access to simultaneous cellular and network measurements, and pharmacological modulations. We propose that by developing and using models with direct links to experiment at multiple levels, which at least include cellular and microcircuit, a cycling can be set up and used to help us determine critical mechanisms underlying neurological disease. We illustrate our proposal using our previously developed inhibitory network models in the context of these whole hippocampus preparations and show the importance of having direct links at multiple levels.

Experimentally constrained CA1 fast-firing parvalbumin-positive interneuron network models exhibit sharp transitions into coherent high frequency rhythms

The coupling of high frequency oscillations (HFOs; >100 Hz) and theta oscillations (3–12 Hz) in the CA1 region of rats increases during REM sleep, indicating that it may play a role in memory processing. However, it is unclear whether the CA1 region itself is capable of providing major contributions to the generation of HFOs, or if they are strictly driven through input projections. Parvalbumin-positive (PV+) interneurons may play an essential role in these oscillations due to their extensive connections with neighboring pyramidal cells, and their characteristic fast-spiking. Thus, we created mathematical network models to investigate the conditions under which networks of CA1 fast-spiking PV+ interneurons are capable of producing high frequency population rhythms. We used whole-cell patch clamp recordings of fast-spiking, PV+ cells in the CA1 region of an intact hippocampal preparation in vitro to derive cellular properties, from which we constrained an Izhikevich-type model. Novel, biologically constrained network models were constructed with these individual cell models, and we investigated networks across a range of experimentally determined excitatory inputs and inhibitory synaptic strengths. For each network, we determined network frequency and coherence. Network simulations produce coherent firing at high frequencies (>90 Hz) for parameter ranges in which PV-PV inhibitory synaptic conductances are necessarily small and external excitatory inputs are relatively large. Interestingly, our networks produce sharp transitions between random and coherent firing, and this sharpness is lost when connectivity is increased beyond biological estimates. Our work suggests that CA1 networks may be designed with mechanisms for quickly gating in and out of high frequency coherent population rhythms, which may be essential in the generation of nested theta/high frequency rhythms.

Cytoarchitectonic and dynamic origins of giant positive local field potentials in the dentate gyrus

To determine why some pathways but not others produce sizable local field potentials (LFPs) and how far from the source can these be recorded, complementary experimental analyses and realistic modeling of specific brain structures are required. In the present study, we combined multiple in vivo linear recordings in rats and a tridimensional finite element model of the dentate gyrus, a curved structure displaying abnormally large positive LFPs. We demonstrate that the polarized dendritic arbour of granule cells (GCs), combined with the curved layered configuration of the population promote the spatial clustering of GC currents in the interposed hilus and project them through the open side at a distance from cell domains. LFPs grow up to 20 times larger than observed in synaptic sites. The dominant positive polarity of hilar LFPs was only produced by the synchronous activation of GCs in both blades by either somatic inhibition or dendritic excitation. Moreover, the corresponding anatomical pathways must project to both blades of the dentate gyrus as even a mild decrease in the spatial synchronization resulted in a dramatic reduction in LFP power in distant sites, yet not in the GC domains. It is concluded that the activation of layered structures may establish sharply delimited spatial domains where synaptic currents from one or another input appear to be segregated according to the topology of afferent pathways and the cytoarchitectonic features of the target population. These also determine preferred directions for volume conduction in the brain, of relevance for interpretation of surface EEG recordings.

Complete classification of the macroscopic behavior of a heterogeneous network of theta neurons

We design and analyze the dynamics of a large network of theta neurons, which are idealized type I neurons. The network is heterogeneous in that it includes both inherently spiking and excitable neurons. The coupling is global, via pulselike synapses of adjustable sharpness. Using recently developed analytical methods, we identify all possible asymptotic states that can be exhibited by a mean field variable that captures the network's macroscopic state. These consist of two equilibrium states that reflect partial synchronization in the network and a limit cycle state in which the degree of network synchronization oscillates in time. Our approach also permits a complete bifurcation analysis, which we carry out with respect to parameters that capture the degree of excitability of the neurons, the heterogeneity in the population, and the coupling strength (which can be excitatory or inhibitory). We find that the network typically tends toward the two macroscopic equilibrium states when the neuron's intrinsic dynamics and the network interactions reinforce one another. In contrast, the limit cycle state, bifurcations, and multistability tend to occur when there is competition among these network features. Finally, we show that our results are exhibited by finite network realizations of reasonable size.

Moving beyond Type I and Type II neuron types

In 1948, Hodgkin delineated different classes of axonal firing.  This has been mathematically translated allowing insight and understanding to emerge.  As such, the terminology of ‘Type I’ and ‘Type II’ neurons is commonplace in the Neuroscience literature today.  Theoretical insights have helped us realize that, for example, network synchronization depends on whether neurons are Type I or Type II.  Mathematical models are precise with analyses (considering Type I/II aspects), but experimentally, the distinction can be less clear.  On the other hand, experiments are becoming more sophisticated in terms of distinguishing and manipulating particular cell types but are limited in terms of being able to consider network aspects simultaneously.   Although there is much work going on mathematically and experimentally, in my opinion it is becoming common that models are either superficially linked with experiment or not described in enough detail to appreciate the biological context.  Overall, we all suffer in terms of impeding our understanding of brain networks and applying our understanding to neurological disease.  I suggest that more modelers become familiar with experimental details and that more experimentalists appreciate modeling assumptions. In other words, we need to move beyond our comfort zones.

EXPONENTIAL TIME DIFFERENCING FOR HODGKIN-HUXLEY-LIKE ODES

Several authors have proposed the use of exponential time differencing (ETD) for Hodgkin-Huxley-like partial and ordinary differential equations (PDEs and ODEs). For Hodgkin-Huxley-like PDEs, ETD is attractive because it can deal effectively with the stiffness issues that diffusion gives rise to. However, large neuronal networks are often simulated assuming "space-clamped" neurons, i.e., using the Hodgkin-Huxley ODEs, in which there are no diffusion terms. Our goal is to clarify whether ETD is a good idea even in that case. We present a numerical comparison of first- and second-order ETD with standard explicit time-stepping schemes (Euler's method, the midpoint method, and the classical fourth-order Runge-Kutta method). We find that in the standard schemes, the stable computation of the very rapid rising phase of the action potential often forces time steps of a small fraction of a millisecond. This can result in an expensive calculation yielding greater overall accuracy than needed. Although it is tempting at first to try to address this issue with adaptive or fully implicit time-stepping, we argue that neither is effective here. The main advantage of ETD for Hodgkin-Huxley-like systems of ODEs is that it allows underresolution of the rising phase of the action potential without causing instability, using time steps on the order of one millisecond. When high quantitative accuracy is not necessary and perhaps, because of modeling inaccuracies, not even useful, ETD allows much faster simulations than standard explicit time-stepping schemes. The second-order ETD scheme is found to be substantially more accurate than the first-order one even for large values of Δt.