On the Role of Theory and Modeling in Neuroscience.

In recent years, the field of neuroscience has gone through rapid experimental advances and a significant increase in the use of quantitative and computational methods. This growth has created a need for clearer analyses of the theory and modeling approaches used in the field. This issue is particularly complex in neuroscience because the field studies phenomena that cross a wide range of scales and often require consideration at varying degrees of abstraction, from precise biophysical interactions to the computations they implement. We argue that a pragmatic perspective of science, in which descriptive, mechanistic, and normative models and theories each play a distinct role in defining and bridging levels of abstraction, will facilitate neuroscientific practice. This analysis leads to methodological suggestions, including selecting a level of abstraction that is appropriate for a given problem, identifying transfer functions to connect models and data, and the use of models themselves as a form of experiment.

Simulation of oscillatory dynamics induced by an approximation of grid cell output.

Grid cells, in entorhinal cortex (EC) and related structures, signal animal location relative to hexagonal tilings of 2D space. A number of modeling papers have addressed the question of how grid firing behaviors emerge using (for example) ideas borrowed from dynamical systems (attractors) or from coupled oscillator theory. Here we use a different approach: instead of asking how grid behavior emerges, we take as a given the experimentally observed intracellular potentials of superficial medial EC neurons during grid firing. Employing a detailed neural circuit model modified from a lateral EC model, we then ask how the circuit responds when group of medial EC principal neurons exhibit such potentials, simultaneously with a simulated theta frequency input from the septal nuclei. The model predicts the emergence of robust theta-modulated gamma/beta oscillations, suggestive of oscillations observed in an in vitro medial EC experimental model (Cunningham, M.O., Pervouchine, D.D., Racca, C., Kopell, N.J., Davies, C.H., Jones, R.S.G., Traub, R.D., and Whittington, M.A. (2006). Neuronal metabolism governs cortical network response state. Proc. Natl. Acad. Sci. U S A 103: 5597-5601). Such oscillations result because feedback interneurons tightly synchronize with each other - despite the varying phases of the grid cells - and generate a robust inhibition-based rhythm. The lack of spatial specificity of the model interneurons is consistent with the lack of spatial periodicity in parvalbumin interneurons observed by Buetfering, C., Allen, K., and Monyer, H. (2014). Parvalbumin interneurons provide grid cell-driven recurrent inhibition in the medial entorhinal cortex. Nat. Neurosci. 17: 710-718. If in vivo EC gamma rhythms arise during exploration as our model predicts, there could be implications for interpreting disrupted spatial behavior and gamma oscillations in animal models of Alzheimer's disease and schizophrenia. Noting that experimental intracellular grid cell potentials closely resemble cortical Up states and Down states, during which fast oscillations also occur during Up states, we propose that the co-occurrence of slow principal cell depolarizations and fast network oscillations is a general property of the telencephalon, in both waking and sleep states.

Processing of cell assemblies in the lateral entorhinal cortex.

There is evidence that olfactory cortex responds to its afferent input with the generation of cell assemblies: collections of principal neurons that fire together over a time scale of tens of ms. If such assemblies form an odor representation, then a fundamental question is how each assembly then induces neuronal activity in downstream structures. We have addressed this question in a detailed model of superficial layers of lateral entorhinal cortex, a recipient of input from olfactory cortex and olfactory bulb. Our results predict that the response of the fan cell subpopulation can be approximated by a relatively simple Boolean process, somewhat along the lines of the McCulloch/Pitts scheme; this is the case because of the sparsity of recurrent excitation amongst fan cells. However, because of recurrent excitatory connections between layer 2 and layer 3 pyramidal cells, synaptic and probably also gap junctional, the response of pyramidal cell subnetworks cannot be so approximated. Because of the highly structured anatomy of entorhinal output projections, our model suggests that downstream targets of entorhinal cortex (dentate gyrus, hippocampal CA3, CA1, piriform cortex, olfactory bulb) receive differentially processed information.

A hypothesis concerning distinct schemes of olfactory activation evoked by perceived versus nonperceived input.

SignificanceThe authors propose that odors are consciously perceived or not, depending on whether the olfactory cortex succeeds in activating the endopiriform nucleus-a structure that, in turn, is capable of activating multiple downstream brain areas. The authors further propose that the cellular mechanisms of endopiriform nucleus activation are an attenuated form of cellular events that occur during epileptic seizure initiation. If correct, the authors' hypothesis could help explain the mechanisms of action of certain general anesthetics.

Cell assembly formation and structure in a piriform cortex model.

The piriform cortex is rich in recurrent excitatory synaptic connections between pyramidal neurons. We asked how such connections could shape cortical responses to olfactory lateral olfactory tract (LOT) inputs. For this, we constructed a computational network model of anterior piriform cortex with 2000 multicompartment, multiconductance neurons (500 semilunar, 1000 layer 2 and 500 layer 3 pyramids; 200 superficial interneurons of two types; 500 deep interneurons of three types; 500 LOT afferents), incorporating published and unpublished data. With a given distribution of LOT firing patterns, and increasing the strength of recurrent excitation, a small number of firing patterns were observed in pyramidal cell networks: first, sparse firings; then temporally and spatially concentrated epochs of action potentials, wherein each neuron fires one or two spikes; then more synchronized events, associated with bursts of action potentials in some pyramidal neurons. We suggest that one function of anterior piriform cortex is to transform ongoing streams of input spikes into temporally focused spike patterns, called here "cell assemblies", that are salient for downstream projection areas.

Alkaline brain pH shift in rodent lithium-pilocarpine model of epilepsy with chronic seizures.

Brain pH is thought to be important in epilepsy. The regulation of brain pH is, however, still poorly understood in animal models of chronic seizures (SZ) as well as in patients with intractable epilepsy. We used chemical exchange saturation transfer (CEST) MRI to noninvasively determine if the pH is alkaline shifted in a rodent model of the mesial temporal lobe (MTL) epilepsy with chronic SZ. Taking advantage of its high spatial resolution, we determined the pH values in specific brain regions believed to be important in this model produced by lithium-pilocarpine injection. All animals developed status epilepticus within 90 min after the lithium-pilocarpine administration, but one animal died within 24 hrs. All the surviving animals developed chronic SZ during the first 2 months. After SZ developed, brain pH was determined in the pilocarpine and control groups (n = 8 each). Epileptiform activity was documented in six pilocarpine rats with scalp EEG. The brain pH was estimated using two methods based on magnetization transfer asymmetry and amide proton transfer ratio. The pH was alkaline shifted in the pilocarpine rats (one outlier excluded) compared to the controls in the hippocampus (7.29 vs 7.17, t-test, p < 0.03) and the piriform cortex (7.34 vs. 7.06, p < 0.005), marginally more alkaline in the thalamus (7.13 vs. 7.01, p < 0.05), but not in the cerebral cortex (7.18 vs. 7.08, p > 0.05). Normalizing the brain pH may lead to an effective non-surgical method for treating intractable epilepsy as it is known that SZ can be eliminated by lowering the pH.

Layer 4 pyramidal neuron dendritic bursting underlies a post-stimulus visual cortical alpha rhythm.

Alpha rhythms (9-11 Hz) are a dominant feature of EEG recordings, particularly over occipital cortex on cessation of a visual stimulation. Little is known about underlying neocortical mechanisms so here we constructed alpha rhythm models that follow cessation of cortical stimulation. The rhythm manifests following a period of gamma frequency activity in local V1 networks in layer 4. It associates with network level bias of excitatory synaptic activity in favour of NMDA- rather than AMPA-mediated signalling and reorganisation of synaptic inhibition in favour of fast GABAA receptor-mediated events. At the cellular level the alpha rhythm depended upon the generation of layer 4 pyramidal neuron dendritic bursting mediated primarily by PPDA-sensitive NR2C/D-containing NMDA receptors, which lack the magnesium-dependent open channel block. Subthreshold potassium conductances are also critical. The rhythm dynamically filters outputs from sensory relay neurons (stellate neurons in layer 4) such that they become temporally uncoupled from downstream population activity.

Epileptic Activity Intrinsically Generated in the Human Cerebellum.

Neoplastic or dysplastic neuronal tissue in the brain stem and cerebellum can become epileptogenic in pediatric patients. However, it is unknown whether such tissue may transform intrinsic properties of the human cerebellum, making it capable of generating epileptic population activity. We noninvasively detected epileptiform signals unaveraged in a pediatric patient with epilepsy due to a tumor in the middle cerebellar peduncle. Analysis of generators of the signals revealed that the cerebellum ipsilateral and contralateral to the tumor was the dominant interictal spike generator and could initiate ictal activity, suggesting that human cerebellum may become capable of intrinsically generating epileptic activity. ANN NEUROL 2020;88:418-422.

Connexin36 localization along axon initial segments in the mammalian CNS.

Electrical synapses formed by gap junctions occur at a variety of neuronal subcellular sites in the mammalian central nervous system (CNS), including at somatic, dendritic and axon terminal compartments. Numerous electrophysiological studies using mice and rats, as well as computer modelling approaches, have predicted the additional occurrence of electrical synapses between axons near their emergence from neuronal somata. Here, we used immunofluorescence methods to search for localization of the neuronal gap junction-forming protein connexin36 (Cx36) along axon initial segments (AISs) labelled for the AIS marker ankyrinG. Immunofluorescent Cx36-puncta were found to be associated with AISs in several CNS regions of mice, including the spinal cord, inferior olive and cerebral cortex. Localization of Cx36-puncta at AISs was confirmed by confocal single scan and 3D imaging, immunofluorescence intensity profiling and high resolution structured illumination microscopy (SIM). AISs measuring up to 30 µm in length displayed typically a single Cx36-punctum and the incidence of these long AISs displaying Cx36-puncta ranged from 3% to 7% in the inferior olive and in various layers of the cerebral cortex. In the inferior olive, the gap junction associated protein zonula occludens-1 (ZO-1) was found to be co-localized with Cx36-puncta on AISs, indicating that these puncta have some of the molecular constituents of gap junctions. Our results add to the neuronal subcellular locations at which Cx36 is deployed, and raise possibilities for its involvement in novel functions in the AIS compartment.

Could electrical coupling contribute to the formation of cell assemblies?

Cell assemblies and central pattern generators (CPGs) are related types of neuronal networks: both consist of interacting groups of neurons whose collective activities lead to defined functional outputs. In the case of a cell assembly, the functional output may be interpreted as a representation of something in the world, external or internal; for a CPG, the output 'drives' an observable (i.e. motor) behavior. Electrical coupling, via gap junctions, is critical for the development of CPGs, as well as for their actual operation in the adult animal. Electrical coupling is also known to be important in the development of hippocampal and neocortical principal cell networks. We here argue that electrical coupling - in addition to chemical synapses - may therefore contribute to the formation of at least some cell assemblies in adult animals.

Seizure initiation in infantile spasms vs. focal seizures: proposed common cellular mechanisms.

Infantile spasms (IS) and seizures with focal onset have different clinical expressions, even when electroencephalography (EEG) associated with IS has some degree of focality. Oddly, identical pathology (with, however, age-dependent expression) can lead to IS in one patient vs. focal seizures in another or even in the same, albeit older, patient. We therefore investigated whether the cellular mechanisms underlying seizure initiation are similar in the two instances: spasms vs. focal. We noted that in-common EEG features can include (i) a background of waves at alpha to delta frequencies; (ii) a period of flattening, lasting about a second or more - the electrodecrement (ED); and (iii) often an interval of very fast oscillations (VFO; ~70 Hz or faster) preceding, or at the beginning of, the ED. With IS, VFO temporally coincides with the motor spasm. What is different between the two conditions is this: with IS, the ED reverts to recurring slow waves, as occurring before the ED, whereas with focal seizures the ED instead evolves into an electrographic seizure, containing high-amplitude synchronized bursts, having superimposed VFO. We used in vitro data to help understand these patterns, as such data suggest cellular mechanisms for delta waves, for VFO, for seizure-related burst complexes containing VFO, and, more recently, for the ED. We propose a unifying mechanistic hypothesis - emphasizing the importance of brain pH - to explain the commonalities and differences of EEG signals in IS versus focal seizures.

Theta/delta coupling across cortical laminae contributes to semantic cognition.

Rhythmic activity in populations of neurons is associated with cognitive and motor function. Our understanding of the neuronal mechanisms underlying these core brain functions has benefitted from demonstrations of cellular, synaptic, and network phenomena, leading to the generation of discrete rhythms at the local network level. However, discrete frequencies of rhythmic activity rarely occur alone. Despite this, little is known about why multiple rhythms are generated together or what mechanisms underlie their interaction to promote brain function. One overarching theory is that different temporal scales of rhythmic activity correspond to communication between brain regions separated by different spatial scales. To test this, we quantified the cross-frequency interactions between two dominant rhythms-theta and delta activity-manifested during magnetoencephalography recordings of subjects performing a word-pair semantic decision task. Semantic processing has been suggested to involve the formation of functional links between anatomically disparate neuronal populations over a range of spatial scales, and a distributed network was manifest in the profile of theta-delta coupling seen. Furthermore, differences in the pattern of theta-delta coupling significantly correlated with semantic outcome. Using an established experimental model of concurrent delta and theta rhythms in neocortex, we show that these outcome-dependent dynamics could be reproduced in a manner determined by the strength of cholinergic neuromodulation. Theta-delta coupling correlated with discrete neuronal activity motifs segregated by the cortical layer, neuronal intrinsic properties, and long-range axonal targets. Thus, the model suggested that local, interlaminar neocortical theta-delta coupling may serve to coordinate both cortico-cortical and cortico-subcortical computations during distributed network activity. NEW & NOTEWORTHY Here, we show, for the first time, that a network of spatially distributed brain regions can be revealed by cross-frequency coupling between delta and theta frequencies in subjects using magnetoencephalography recording during a semantic decision task. A biological model of this cross-frequency coupling suggested an interlaminar, cell-specific division of labor within the neocortex may serve to route the flow of cortico-cortical and cortico-subcortical information to promote such spatially distributed, functional networks.

Electrical coupling between hippocampal neurons: contrasting roles of principal cell gap junctions and interneuron gap junctions.

There is considerable experimental evidence, anatomical and physiological, that gap junctions exist in the hippocampus. Electrical coupling through these gap junctions may be divided into three types: between principal neurons, between interneurons and at mixed chemical (glutamatergic)/electrical synapses. An approach, combining in vitro experimental with modeling techniques, sheds some light on the functional consequences of electrical coupling, for network oscillations and for seizures. Additionally, in vivo experiments, using mouse connexin knockouts, suggest that the presence of electrical coupling is important for optimal performance on selected behavioral tasks; however, the interpretation of such data, in cellular terms, has so far proven difficult. Given that invertebrate central pattern generators so often depend on both chemical and electrical synapses, our hypothesis is that hippocampus-mediated and -influenced behaviors will act likewise. Experiments, likely hard ones, will be required to test this intuition.

Enhanced interlaminar excitation or reduced superficial layer inhibition in neocortex generates different spike-and-wave-like electrographic events in vitro.

Acute in vitro models have revealed a great deal of information about mechanisms underlying many types of epileptiform activity. However, few examples exist that shed light on spike-and-wave (SpW) patterns of pathological activity. SpW are seen in many epilepsy syndromes, both generalized and focal, and manifest across the entire age spectrum. They are heterogeneous in terms of their severity, symptom burden, and apparent anatomical origin (thalamic, neocortical, or both), but any relationship between this heterogeneity and underlying pathology remains elusive. In this study we demonstrate that physiological delta-frequency rhythms act as an effective substrate to permit modeling of SpW of cortical origin and may help to address this issue. For a starting point of delta activity, multiple subtypes of SpW could be modeled computationally and experimentally by either enhancing the magnitude of excitatory synaptic events ascending from neocortical layer 5 to layers 2/3 or selectively modifying superficial layer GABAergic inhibition. The former generated SpW containing multiple field spikes with long interspike intervals, whereas the latter generated SpW with short-interval multiple field spikes. Both types had different laminar origins and each disrupted interlaminar cortical dynamics in a different manner. A small number of examples of human recordings from patients with different diagnoses revealed SpW subtypes with the same temporal signatures, suggesting that detailed quantification of the pattern of spikes in SpW discharges may be a useful indicator of disparate underlying epileptogenic pathologies. NEW & NOTEWORTHY Spike-and-wave-type discharges (SpW) are a common feature in many epilepsies. Their electrographic manifestation is highly varied, as are available genetic clues to associated underlying pathology. Using computational and in vitro models, we demonstrate that distinct subtypes of SpW are generated by lamina-selective disinhibition or enhanced interlaminar excitation. These subtypes could be detected in at least some noninvasive patient recordings, suggesting more detailed analysis of SpW may be useful in determining clinical pathology.

A future for neuronal oscillation research.

Neuronal oscillations represent the most obvious feature of electrical activity in the brain. They are linked in general with global brain state (awake, asleep, etc.) and specifically with organisation of neuronal outputs during sensory perception and cognitive processing. Oscillations can be generated by individual neurons on the basis of interaction between inputs and intrinsic conductances but are far more commonly seen at the local network level in populations of interconnected neurons with diverse arrays of functional properties. It is at this level that the brain's rich and diverse library of oscillatory time constants serve to temporally organise large-scale neural activity patterns. The discipline is relatively mature at the microscopic (cell, local network) level - although novel discoveries are still commonplace - but requires a far greater understanding of mesoscopic and macroscopic brain dynamics than we currently hold. Without this, extrapolation from the temporal properties of neurons and their communication strategies up to whole brain function will remain largely theoretical. However, recent advances in large-scale neuronal population recordings and more direct, higher fidelity, non-invasive measurement of whole brain function suggest much progress is just around the corner.

Does Epileptiform Activity Represent a Failure of Neuromodulation to Control Central Pattern Generator-Like Neocortical Behavior?

Rhythmic motor patterns in invertebrates are often driven by specialized "central pattern generators" (CPGs), containing small numbers of neurons, which are likely to be "identifiable" in one individual compared with another. The dynamics of any particular CPG lies under the control of modulatory substances, amines, or peptides, entering the CPG from outside it, or released by internal constituent neurons; consequently, a particular CPG can generate a given rhythm at different frequencies and amplitudes, and perhaps even generate a repertoire of distinctive patterns. The mechanisms exploited by neuromodulators in this respect are manifold: Intrinsic conductances (e.g., calcium, potassium channels), conductance state of postsynaptic receptors, degree of plasticity, and magnitude and kinetics of transmitter release can all be affected. The CPG concept has been generalized to vertebrate motor pattern generating circuits (e.g., for locomotion), which may contain large numbers of neurons - a construct that is sensible, if there is enough redundancy: that is, the large number of neurons consists of only a small number of classes, and the cells within any one class act stereotypically. Here we suggest that CPG and modulator ideas may also help to understand cortical oscillations, normal ones, and particularly transition to epileptiform pathology. Furthermore, in the case illustrated, the mechanism of the transition appears to be an exaggerated form of a normal modulatory action used to influence sensory processing.

Aberrant Network Activity in Schizophrenia.

Brain dynamic changes associated with schizophrenia are largely equivocal, with interpretation complicated by many factors, such as the presence of therapeutic agents and the complex nature of the syndrome itself. Evidence for a brain-wide change in individual network oscillations, shared by all patients, is largely equivocal, but stronger for lower (delta) than for higher (gamma) bands. However, region-specific changes in rhythms across multiple, interdependent, nested frequencies may correlate better with pathology. Changes in synaptic excitation and inhibition in schizophrenia disrupt delta rhythm-mediated cortico-cortical communication, while enhancing thalamocortical communication in this frequency band. The contrasting relationships between delta and higher frequencies in thalamus and cortex generate frequency mismatches in inter-regional connectivity, leading to a disruption in temporal communication between higher-order brain regions associated with mental time travel.

Electrographic waveform structure predicts laminar focus location in a model of temporal lobe seizures in vitro.

Temporal lobe epilepsy is the most common form of partial-onset epilepsy and accounts for the majority of adult epilepsy cases in most countries. A critical role for the hippocampus (and to some extent amygdala) in the pathology of these epilepsies is clear, with selective removal of these regions almost as effective as temporal lobectomy in reducing subsequent seizure risk. However, there is debate about whether hippocampus is 'victim' or 'perpetrator': The structure is ideally placed to 'broadcast' epileptiform activity to a great many other brain regions, but removal often leaves epileptiform events still occurring in cortex, particularly in adjacent areas, and recruitment of the hippocampus into seizure-like activity has been shown to be difficult in clinically-relevant models. Using a very simple model of acute epileptiform activity with known, single primary pathology (GABAA Receptor partial blockade), we track the onset and propagation of epileptiform events in hippocampus, parahippocampal areas and neocortex. In this model the hippocampus acts as a potential seizure focus for the majority of observed events. Events with hippocampal focus were far more readily propagated throughout parahippocampal areas and into neocortex than vice versa. The electrographic signature of events of hippocampal origin was significantly different to those of primary neocortical origin - a consequence of differential laminar activation. These data confirm the critical role of the hippocampus in epileptiform activity generation in the temporal lobe and suggest the morphology of non-invasive electrical recording of neocortical interictal events may be useful in confirming this role.

What is a seizure network? Very fast oscillations at the interface between normal and epileptic brain.

Although there is a great multiplicity of normal brain electrical activities, one can observe defined, relatively abrupt, transitions between apparently normal rhythms and clearly abnormal, higher amplitude, "epileptic" signals; transitions occur over tens of ms to many seconds. Transitional activity typically consists of low-amplitude very fast oscillations (VFO). Examination of this VFO provides insight into system parameters that differentiate the "normal" from the "epileptic." Remarkably, VFO in vitro is generated by principal neuron gap junctions, and occurs readily when chemical synapses are suppressed, tissue pH is elevated, and [Ca(2+)]o is low. Because VFO originates in principal cell axons that fire at high frequencies, excitatory synapses may experience short-term plasticity. If the latter takes the form of potentiation of recurrent synapses on principal cells, and depression of these on inhibitory interneurons, then the stage is set for synchronized bursting - if [Ca(2+)]o recovers sufficiently. Our hypothesis can be tested (in part) in patients, once it is possible to measure brain tissue parameters (pH, [Ca(2+)]o) simultaneously with ECoG.