Propagating neuronal discharges in neocortical slices: computational and experimental study

Mechanistic role of alpha oscillations in a computational model of working memory

Brain oscillations are believed to be involved in the different operations necessary to manipulate information during working memory tasks. We propose a mechanistic role for the observed inhibition effect of the alpha rhythm based on its interference with the theta rhythm. Using the Lisman-Idiart model for multi-item working memory, we show that the interaction between these two oscillations is capable of creating a long lasting destructive interference that prevents the cyclic reactivation of neuronal ensembles and, as a consequence, memory maintenance. Additionally, to ensure robustness we propose a modular version of the model and implement oscillations as traveling waves. Using this model, we show that the interactions between theta and gamma determine the allocation of multiple memories in distinct modules, while the interference between theta and alpha disrupts the maintenance of the information already stored in them. The effect of alpha in erasing or blocking storage is robust and seems fairly independent of frequency, as long as it stays within the alpha range. This model helps us to understand why the alpha and theta oscillations, which have close frequency bands, could have opposite roles in working memory.

The inhibitory control of traveling waves in cortical networks

Propagating waves of activity can be evoked and can occur spontaneously in vivo and in vitro in cerebral cortex. These waves are thought to be instrumental in the propagation of information across cortical regions and as a means to modulate the sensitivity of neurons to subsequent stimuli. In normal tissue, the waves are sparse and tightly controlled by inhibition and other negative feedback processes. However, alterations of this balance between excitation and inhibition can lead to pathological behavior such as seizure-type dynamics (with low inhibition) or failure to propagate (with high inhibition). We develop a spiking one-dimensional network of neurons to explore the reliability and control of evoked waves and compare this to a cortical slice preparation where the excitability can be pharmacologically manipulated. We show that the waves enhance sensitivity of the cortical network to stimuli in specific spatial and temporal ways. To gain further insight into the mechanisms of propagation and transitions to pathological behavior, we derive a mean-field model for the synaptic activity. We analyze the mean-field model and a piece-wise constant approximation of it and study the stability of the propagating waves as spatial and temporal properties of the inhibition are altered. We show that that the transition to seizure-like activity is gradual but that the loss of propagation is abrupt and can occur via either the loss of existence of the wave or through a loss of stability leading to complex patterns of propagation.

Fractional-Order Traveling Wave Approximations for a Fractional-Order Neural Field Model

In this work, we establish a fractional-order neural field mathematical model with Caputo's fractional derivative temporal order α considering 0 < α < 2, to analyze the effect of fractional-order on cortical wave features observed preceding seizure termination. The importance of this incorporation relies on the theoretical framework established by fractional-order derivatives in which memory and hereditary properties of a system are considered. Employing Mittag-Leffler functions, we first obtain approximate fractional-order solutions that provide information about the initial wave dynamics in a fractional-order frame. We then consider the Adomian decomposition method to approximate pulse solutions in a wider range of orders and longer times. The former approach establishes a direct way to investigate the initial relationships between fractional-order and wave features, such as wave speed and wave width. In contrast, the latter approach displays wave propagation dynamics in different fractional orders for longer times. Using the previous two approaches, we establish approximate wave solutions with characteristics consistent with in vivo cortical waves preceding seizure termination. In our analysis, we find consistent differences in the initial effect of the fractional-order on the features of wave speed and wave width, depending on whether α <1 or α>1. Both cases can model the shape of cortical wave propagation for different fractional-orders at the cost of modifying the wave speed. Our results also show that the effect of fractional-order on wave width depends on the synaptic threshold and the synaptic connectivity extent. Fractional-order derivatives have been interpreted as the memory trace of the system. This property and the results of our analysis suggest that fractional-order derivatives and neuronal collective memory modify cortical wave features.

Ictal wavefront propagation in slices and simulations with conductance-based refractory density model

The mechanisms determining ictal discharge (ID) propagation are still not clear. In the present study, we aimed to examine these mechanisms in animal and mathematical models of epileptiform activity. Using double-patch and extracellular potassium ion concentration recordings in rat hippocampal-cortical slices, we observed that IDs moved at a speed of about 1 mm/s or less. The mechanisms of such slow propagation have been studied with a mathematical, conductance-based refractory density (CBRD) model that describes the GABA- and glutamatergic neuronal populations’ interactions and ion dynamics in brain tissue. The modeling study reveals two main factors triggerring IDs: (i) increased interneuronal activity leading to chloride ion accumulation and a consequent depolarizing GABAergic effect and (ii) the elevation of extracellular potassium ion concentration. The local synaptic transmission followed by local potassium ion extrusion and GABA receptor-mediated chloride ion accumulation underlies the ID wavefront’s propagation. In contrast, potassium ion diffusion in the extracellular space is slower and does not affect ID’s speed. The short discharges, constituting the ID, propagate much faster than the ID front. The accumulation of sodium ions inside neurons due to their hyperactivity and glutamatergic currents boosts the Na⁺/K⁺ pump, which terminates the ID. Knowledge of the mechanism of ID generation and propagation contributes to the development of new treatments against epilepsy.

During an epileptic seizure, neuronal excitation spreads across the brain tissue and is accompanied by significant changes in ionic concentrations. Ictal discharge front spreads at low speeds, less than 1 mm/s. Mechanisms underlying this phenomenon are not yet well understood. We study these mechanisms using electrophysiological recordings in brain slices and computer simulations. Our detailed biophysical model describing neuronal populations’ interaction, spatial propagation, and ionic dynamics reproduces the generation and propagation of spontaneously repeating ictal discharges. The simulations are consistent with our recordings of the electrical activity and the extracellular potassium ion concentration. We distinguished between the two alternative mechanisms of the ictal wavefront propagation: (i) the diffusion of potassium ions released from excited neurons, which depolarizes distant neurons and thus supports excitation, and (ii) the axonal spread of excitation followed by the local extracellular potassium ion accumulation that supports the excitation. Our simulations provide evidence in favor of the latter mechanism. Our experiment-based modeling contributes to a mathematical description of brain tissue functioning and potentially contributes to developing new treatments against epilepsy.

Traveling Waves in Quasi-One-Dimensional Neuronal Minicolumns

Traveling waves of neuronal activity in the cortex have been observed in vivo. These traveling waves have been correlated to various features of observed cortical dynamics, including spike timing variability and correlated fluctuations in neuron membrane potential. Although traveling waves are typically studied as either strictly one-dimensional or two-dimensional excitations, here we investigate the conditions for the existence of quasi-one-dimensional traveling waves that could be sustainable in parts of the brain containing cortical minicolumns. For that, we explore a quasi-one-dimensional network of heterogeneous neurons with a biologically influenced computational model of neuron dynamics and connectivity. We find that background stimulus reliably evokes traveling waves in networks with local connectivity between neurons. We also observe traveling waves in fully connected networks when a model for action potential propagation speed is incorporated. The biological properties of the neurons influence the generation and propagation of the traveling waves. Our quasi-one-dimensional model is not only useful for studying the basic properties of traveling waves in neuronal networks; it also provides a simplified representation of possible wave propagation in columnar or minicolumnar networks found in the cortex.

Patient-Specific Network Connectivity Combined With a Next Generation Neural Mass Model to Test Clinical Hypothesis of Seizure Propagation

Dynamics underlying epileptic seizures span multiple scales in space and time, therefore, understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. In this view, mathematical models have been developed, ranging from single neuron to neural population. In this study, we consider a neural mass model able to exactly reproduce the dynamics of heterogeneous spiking neural networks. We combine mathematical modeling with structural information from non invasive brain imaging, thus building large-scale brain network models to explore emergent dynamics and test the clinical hypothesis. We provide a comprehensive study on the effect of external drives on neuronal networks exhibiting multistability, in order to investigate the role played by the neuroanatomical connectivity matrices in shaping the emergent dynamics. In particular, we systematically investigate the conditions under which the network displays a transition from a low activity regime to a high activity state, which we identify with a seizure-like event. This approach allows us to study the biophysical parameters and variables leading to multiple recruitment events at the network level. We further exploit topological network measures in order to explain the differences and the analogies among the subjects and their brain regions, in showing recruitment events at different parameter values. We demonstrate, along with the example of diffusion-weighted magnetic resonance imaging (dMRI) connectomes of 20 healthy subjects and 15 epileptic patients, that individual variations in structural connectivity, when linked with mathematical dynamic models, have the capacity to explain changes in spatiotemporal organization of brain dynamics, as observed in network-based brain disorders. In particular, for epileptic patients, by means of the integration of the clinical hypotheses on the epileptogenic zone (EZ), i.e., the local network where highly synchronous seizures originate, we have identified the sequence of recruitment events and discussed their links with the topological properties of the specific connectomes. The predictions made on the basis of the implemented set of exact mean-field equations turn out to be in line with the clinical pre-surgical evaluation on recruited secondary networks.

The Effect of Anti-seizure Medications on the Propagation of Epileptic Activity: A Review

The propagation of epileptiform events is a highly interesting phenomenon from the pathophysiological point of view, as it involves several mechanisms of recruitment of neural networks. Extensive in vivo and in vitro research has been performed, suggesting that multiple networks as well as cellular candidate mechanisms govern this process, including the co-existence of wave propagation, coupled oscillator dynamics, and more. The clinical importance of seizure propagation stems mainly from the fact that the epileptic manifestations cannot be attributed solely to the activity in the seizure focus itself, but rather to the propagation of epileptic activity to other brain structures. Propagation, especially when causing secondary generalizations, poses a risk to patients due to recurrent falls, traumatic injuries, and poor neurological outcome. Anti-seizure medications (ASMs) affect propagation in diverse ways and with different potencies. Importantly, for drug-resistant patients, targeting seizure propagation may improve the quality of life even without a major reduction in simple focal events. Motivated by the extensive impact of this phenomenon, we sought to review the literature regarding the propagation of epileptic activity and specifically the effect of commonly used ASMs on it. Based on this body of knowledge, we propose a novel classification of ASMs into three main categories: major, minor, and intermediate efficacy in reducing the propagation of epileptiform activity.

Plastic systemic inhibition controls amplitude while allowing phase pattern in a stochastic neural field model

We investigate oscillatory phase pattern formation and amplitude control for a linearized stochastic neuron field model by simulating Mexican-hat-coupled stochastic processes. We find, for several choices of parameters, that spatial pattern formation in the temporal phases of the coupled processes occurs if and only if their amplitudes are allowed to grow unrealistically large. Stimulated by recent work on homeostatic inhibitory plasticity, we introduce static and plastic (adaptive) systemic inhibitory mechanisms to keep the amplitudes stochastically bounded. We find that systems with static inhibition exhibited bounded amplitudes but no sustained phase patterns. With plastic systemic inhibition, on the other hand, the resulting systems exhibit both bounded amplitudes and sustained phase patterns. These results demonstrate that plastic inhibitory mechanisms in neural field models can dynamically control amplitudes while allowing patterns of phase synchronization to develop. Similar mechanisms of plastic systemic inhibition could play a role in regulating oscillatory functioning in the brain.

Empirically constrained network models for contrast-dependent modulation of gamma rhythm in V1

Gamma oscillations are thought to play a key role in neuronal network function and neuronal communication, yet the underlying generating mechanisms have not been fully elucidated to date. At least partly, this may be due to the fact that even in simple network models of interconnected inhibitory (I) and excitatory (E) neurons, many parameters remain unknown and are set based on practical considerations or by convention. Here, we mitigate this problem by requiring PING (Pyramidal Interneuron Network Gamma) models to simultaneously satisfy a broad set of criteria for realistic behaviour based on empirical data spanning both the single unit (spikes) and local population (LFP) levels while unknown parameters are varied. By doing so, we were able to constrain the parameter ranges and select empirically valid models. The derived model constraints implied weak rather than strong PING as the generating mechanism for gamma, connectivity between E and I neurons within specific bounds, and variations of the external input to E but not I neurons. Constrained models showed valid behaviours, including gamma frequency increases with contrast and power saturation or decay at high contrasts. Using an empirically-validated model we studied the route to gamma instability at high contrasts. This involved increased heterogeneity of E neurons with increasing input triggering a breakdown of I neuron pacemaker function. Further, we illustrate the model's capacity to resolve disputes in the literature concerning gamma oscillation properties and GABA conductance proxies. We propose that the models derived in our study will be useful for other modelling studies, and that our approach to the empirical constraining of PING models can be expanded when richer empirical datasets become available. As local gamma networks are the building blocks of larger networks that aim to understand complex cognition through their interactions, there is considerable value in improving our models of these building blocks.

Isoflurane-Induced Burst Suppression Is a Thalamus-Modulated, Focal-Onset Rhythm With Persistent Local Asynchrony and Variable Propagation Patterns in Rats

Background: Inhalational anesthetic-induced burst suppression (BS) is classically considered a bilaterally synchronous rhythm. However, local asynchrony has been predicted in theoretical studies and reported in patients with pre-existing focal pathology. Method: We used high-speed widefield calcium imaging to study the spatiotemporal dynamics of isoflurane-induced BS in rats. Results: We found that isoflurane-induced BS is not a globally synchronous rhythm. In the neocortex, neural activity first emerged in a spatially shifting, variably localized focus. Subsequent propagation across the whole cortex was rapid, typically within <100 milliseconds, giving the superficial resemblance to global synchrony. Neural activity remained locally asynchronous during the bursts, forming complex recurrent propagating waves. Despite propagation variability, spatial sequences of burst propagation were largely preserved between the hemispheres, and neural activity was highly correlated between the homotopic areas. The critical role of the thalamus in cortical burst initiation was demonstrated by using unilateral thalamic tetrodotoxin injection. Conclusion: The classical impression that anesthetics-induced BS is a state of global brain synchrony is inaccurate. Bursts are a series of shifting local cortical events facilitated by thalamic projection that unfold as rapid, bilaterally asynchronous propagating waves.

Energy features in spontaneous up and down oscillations

Spontaneous brain activities consume most of the brain's energy. So if we want to understand how the brain operates, we must take into account these spontaneous activities. Up and down transitions of membrane potentials are considered to be one of significant spontaneous activities. This kind of oscillation always shows bistable and bimodal distribution of membrane potentials. Our previous theoretical studies on up and down oscillations mainly looked at the ion channel dynamics. In this paper, we focus on energy feature of spontaneous up and down transitions based on a network model and its simulation. The simulated results indicate that the energy is a robust index and distinguishable of excitatory and inhibitory neurons. Meanwhile, one the whole, energy consumption of neurons shows bistable feature and bimodal distribution as well as the membrane potential, which turns out that the indicator of energy consumption encodes up and down states in this spontaneous activity. In detail, energy consumption mainly occurs during up states temporally, and mostly concentrates inside neurons rather than synapses spatially. The stimulation related energy is small, indicating that energy consumption is not driven by external stimulus, but internal spontaneous activity. This point of view is also consistent with brain imaging results. Through the observation and analysis of the findings, we prove the validity of the model again, and we can further explore the energy mechanism of more spontaneous activities.

Slow Waves in Cortical Slices: How Spontaneous Activity is Shaped by Laminar Structure

Cortical slow oscillations (SO) of neural activity spontaneously emerge and propagate during deep sleep and anesthesia and are also expressed in isolated brain slices and cortical slabs. We lack full understanding of how SO integrate the different structural levels underlying local excitability of cell assemblies and their mutual interaction. Here, we focus on ongoing slow waves (SWs) in cortical slices reconstructed from a 16-electrode array designed to probe the neuronal activity at multiple spatial scales. In spite of the variable propagation patterns observed, we reproducibly found a smooth strip of loci leading the SW fronts, overlapping cortical layers 4 and 5, along which Up states were the longest and displayed the highest firing rate. Propagation modes were uncorrelated in time, signaling a memoryless generation of SWs. All these features could be modeled by a multimodular large-scale network of spiking neurons with a specific balance between local and intermodular connectivity. Modules work as relaxation oscillators with a weakly stable Down state and a peak of local excitability to model layers 4 and 5. These conditions allow for both optimal sensitivity to the network structure and richness of propagation modes, both of which are potential substrates for dynamic flexibility in more general contexts.

Impact of targeted attack on the spontaneous activity in spatial and biologically-inspired neuronal networks

We study the structural and dynamical consequences of damage in spatial neuronal networks. Inspired by real in vitro networks, we construct directed networks embedded in a two-dimensional space and follow biological rules for designing the wiring of the system. As a result, synthetic cultures display strong metric correlations similar to those observed in real experiments. In its turn, neuronal dynamics is incorporated through the Izhikevich model adopting the parameters derived from observation in real cultures. We consider two scenarios for damage, targeted attacks on those neurons with the highest out-degree and random failures. By analyzing the evolution of both the giant connected component and the dynamical patterns of the neurons as nodes are removed, we observe that network activity halts for a removal of 50% of the nodes in targeted attacks, much lower than the 70% node removal required in the case of random failures. Notably, the decrease of neuronal activity is not gradual. Both damage scenarios portray "boosts" of activity just before full silencing that are not present in equivalent random (Erdös-Rényi) graphs. These boosts correspond to small, spatially compact subnetworks that are able to maintain high levels of activity. Since these subnetworks are absent in the equivalent random graphs, we hypothesize that metric correlations facilitate the existence of local circuits sufficiently integrated to maintain activity, shaping an intrinsic mechanism for resilience.

Complex Dynamics of Propagating Waves in a Two-Dimensional Neural Field

Propagating waves with complex dynamics have been widely observed in neural population activity. To understand their formation mechanisms, we investigate a type of two-dimensional neural field model by systematically varying its recurrent excitatory and inhibitory inputs. We show that the neural field model exhibits a rich repertoire of dynamical activity states when the relevant strength of excitation and inhibition is increased, ranging from localized rotating and traveling waves to global waves. Particularly, near the transition between stable states of rotating and traveling waves, the model exhibits a bistable state; that is, both the rotating and the traveling waves can exist, and the inclusion of noise can induce spontaneous transitions between them. Furthermore, we demonstrate that when there are multiple propagating waves, they exhibit rich collective propagation dynamics with variable propagating speeds and trajectories. We use techniques from time series analysis such detrended fluctuation analysis to characterize the effect of the strength of excitation and inhibition on these collective dynamics, which range from purely random motion to motion with long-range spatiotemporal correlations. These results provide insights into the possible contribution of excitation and inhibition toward a range of previously observed spatiotemporal wave phenomena.

Gap junctions set the speed and nucleation rate of stage I retinal waves

Spontaneous waves in the developing retina are essential in the formation of the retinotopic mapping in the visual system. From experiments in rabbits, it is known that the earliest type of retinal waves (stage I) is nucleated spontaneously, propagates at a speed of 451±91 μm/sec and relies on gap junction coupling between ganglion cells. Because gap junctions (electrical synapses) have short integration times, it has been argued that they cannot set the low speed of stage I retinal waves. Here, we present a theoretical study of a two-dimensional neural network of the ganglion cell layer with gap junction coupling and intrinsic noise. We demonstrate that this model can explain observed nucleation rates as well as the comparatively slow propagation speed of the waves. From the interaction between two coupled neurons, we estimate the wave speed in the model network. Furthermore, using simulations of small networks of neurons (N≤260), we estimate the nucleation rate in the form of an Arrhenius escape rate. These results allow for informed simulations of a realistically sized network, yielding values of the gap junction coupling and the intrinsic noise level that are in a physiologically plausible range.

Mode of seizure inhibition by sodium channel blockers, an SV2A ligand, and an AMPA receptor antagonist in a rat amygdala kindling model

PURPOSE

A number of antiepileptic drugs (AEDs) with a variety of modes of action, are effective in treating focal seizures. Several AEDs, such as perampanel (PER), levetiracetam (LEV), lacosamide (LCM), lamotrigine (LTG), and carbamazepine (CBZ), have been shown to elevate the seizure threshold in kindling models. These AEDs are clinically effective, but differences exist in the anti-seizure profiles of drugs with similar modes of action. Therefore, we hypothesized that there are differences in how these AEDs affect seizures. Here, we evaluated the effects of AEDs on various seizure parameters in a rat amygdala kindling model upon stimulation at the after-discharge threshold (ADT) and at three-times the ADT (3xADT) to characterize the differences in the effects of these AEDs.

METHODS

PER, LEV, LCM, LTG, CBZ, or vehicle was administered intraperitoneally to fully kindled rats. Changes in Racine seizure score, after-discharge duration (ADD), and latency to Racine score 4 generalized seizure (S₄L) were measured to assess differences in the modes of seizure inhibition among the AEDs. Stimulation at 3xADT was used to eliminate the influence of any AED-induced elevation of the seizure threshold on these parameters.

RESULTS

PER, LEV, LCM, LTG, and CBZ significantly reduced the seizure score from Racine score 5 after stimulation at the ADT; this effect was lost with LEV and LTG after stimulation at 3xADT. PER and LEV significantly shortened the ADD when the seizure focus was stimulated at the ADT, whereas LCM, LTG, and CBZ did not. LEV, LCM, LTG, and CBZ failed to shorten the ADD upon stimulation at 3xADT. PER dose-dependently and significantly increased S₄L, even at doses that were ineffective for seizure score reduction, after stimulation at both the ADT and 3xADT. LEV and LTG significantly increased S₄L after stimulation at the ADT, whereas LCM and CBZ did not significantly increase S₄L at any of the doses tested.

CONCLUSIONS

The sodium channel blockers (LCM, LTG, and CBZ) appeared to act by elevation of the seizure threshold via reduction of neuronal excitability, whereas the AMPA receptor antagonist (PER) and the SV2A ligand (LEV), as well as LTG, exerted their effects through the weakening of synaptic transmission in neuronal networks at the seizure focus. Maintenance of the effect of PER even at 3xADT suggests direct and strong modulation of excitatory synaptic transmission by PER, both at the focus and along the seizure propagation route. These findings may provide further rationale for usage of AEDs beyond their respective modes of action.

Cellular switches orchestrate rhythmic circuits

Small inhibitory neuronal circuits have long been identified as key neuronal motifs to generate and modulate the coexisting rhythms of various motor functions. Our paper highlights the role of a cellular switching mechanism to orchestrate such circuits. The cellular switch makes the circuits reconfigurable, robust, adaptable, and externally controllable. Without this cellular mechanism, the circuit rhythms entirely rely on specific tunings of the synaptic connectivity, which makes them rigid, fragile, and difficult to control externally. We illustrate those properties on the much studied architecture of a small network controlling both the pyloric and gastric rhythms of crabs. The cellular switch is provided by a slow negative conductance often neglected in mathematical modeling of central pattern generators. We propose that this conductance is simple to model and key to computational studies of rhythmic circuit neuromodulation.

Next-generation neural field model: The evolution of synchrony within patterns and waves

Neural field models are commonly used to describe wave propagation and bump attractors at a tissue level in the brain. Although motivated by biology, these models are phenomenological in nature. They are built on the assumption that the neural tissue operates in a near synchronous regime, and hence, cannot account for changes in the underlying synchrony of patterns. It is customary to use spiking neural network models when examining within population synchronization. Unfortunately, these high-dimensional models are notoriously hard to obtain insight from. In this paper, we consider a network of θ-neurons, which has recently been shown to admit an exact mean-field description in the absence of a spatial component. We show that the inclusion of space and a realistic synapse model leads to a reduced model that has many of the features of a standard neural field model coupled to a further dynamical equation that describes the evolution of network synchrony. Both Turing instability analysis and numerical continuation software are used to explore the existence and stability of spatiotemporal patterns in the system. In particular, we show that this new model can support states above and beyond those seen in a standard neural field model. These states are typified by structures within bumps and waves showing the dynamic evolution of population synchrony.

Suppression of Parkinsonian Beta Oscillations by Deep Brain Stimulation: Determination of Effective Protocols

A neural field model of the corticothalamic-basal ganglia system is developed that describes enhanced beta activity within subthalamic and pallidal circuits in Parkinson's disease (PD) via system resonances. A model of deep brain stimulation (DBS) of typical clinical targets, the subthalamic nucleus (STN) and globus pallidus internus (GPi), is added and studied for several distinct stimulation protocols that are used for treatment of the motor symptoms of PD and that reduce pathological beta band activity (13-30 Hz) in the corticothalamic-basal ganglia network. The resulting impact of DBS on enhanced beta activity in the STN and GPi, as well as cortico-subthalamic and cortico-pallidal coherence, are studied. Both STN-DBS and GPi-DBS are found to be effective for suppressing peak STN and GPi power in the beta band, with GPi-DBS being slightly more effective in both the STN and the GPi for all stimulus protocols tested. The largest decrease in cortico-STN coherence is observed during STN-DBS, whereas GPi-DBS is most effective for reducing cortico-GPi coherence. A reduction of the pathologically large STN connection strengths that define the parkinsonian state results in enhanced 6 Hz activity and could thus represent a compensatory mechanism that has the side effect of driving parkinsonian tremor-like oscillations. This model provides a method for systematically testing effective DBS protocols that agrees with experimental and clinical findings. Furthermore, the model suggests GPi-DBS and STN-DBS have distinct impacts on elevated synchronization between the basal ganglia and motor cortex in PD.

Multivariate regression methods for estimating velocity of ictal discharges from human microelectrode recordings

OBJECTIVE

Epileptiform discharges, an electrophysiological hallmark of seizures, can propagate across cortical tissue in a manner similar to traveling waves. Recent work has focused attention on the origination and propagation patterns of these discharges, yielding important clues to their source location and mechanism of travel. However, systematic studies of methods for measuring propagation are lacking.

APPROACH

We analyzed epileptiform discharges in microelectrode array recordings of human seizures. The array records multiunit activity and local field potentials at 400 micron spatial resolution, from a small cortical site free of obstructions. We evaluated several computationally efficient statistical methods for calculating traveling wave velocity, benchmarking them to analyses of associated neuronal burst firing.

MAIN RESULTS

Over 90% of discharges met statistical criteria for propagation across the sampled cortical territory. Detection rate, direction and speed estimates derived from a multiunit estimator were compared to four field potential-based estimators: negative peak, maximum descent, high gamma power, and cross-correlation. Interestingly, the methods that were computationally simplest and most efficient (negative peak and maximal descent) offer non-inferior results in predicting neuronal traveling wave velocities compared to the other two, more complex methods. Moreover, the negative peak and maximal descent methods proved to be more robust against reduced spatial sampling challenges. Using least absolute deviation in place of least squares error minimized the impact of outliers, and reduced the discrepancies between local field potential-based and multiunit estimators.

SIGNIFICANCE

Our findings suggest that ictal epileptiform discharges typically take the form of exceptionally strong, rapidly traveling waves, with propagation detectable across millimeter distances. The sequential activation of neurons in space can be inferred from clinically-observable EEG data, with a variety of straightforward computation methods available. This opens possibilities for systematic assessments of ictal discharge propagation in clinical and research settings.

The effect of inhibition on the existence of traveling wave solutions for a neural field model of human seizure termination

In this paper we study the influence of inhibition on an activity-based neural field model consisting of an excitatory population with a linear adaptation term that directly regulates the activity of the excitatory population. Such a model has been used to replicate traveling wave data as observed in high density local field potential recordings (González-Ramírez et al. PLoS Computational Biology, 11(2), e1004065, 2015). In this work, we show that by adding an inhibitory population to this model we can still replicate wave properties as observed in human clinical data preceding seizure termination, but the parameter range over which such waves exist becomes more restricted. This restriction depends on the strength of the inhibition and the timescale at which the inhibition acts. In particular, if inhibition acts on a slower timescale relative to excitation then it is possible to still replicate traveling wave patterns as observed in the clinical data even with a relatively strong effect of inhibition. However, if inhibition acts on the same timescale as the excitation, or faster, then traveling wave patterns with the desired characteristics cease to exist when the inhibition becomes sufficiently strong.

Quantitative theory of deep brain stimulation of the subthalamic nucleus for the suppression of pathological rhythms in Parkinson's disease

Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is modeled to explore the mechanisms of this effective, but poorly understood, treatment for motor symptoms of drug-refractory Parkinson's disease and dystonia. First, a neural field model of the corticothalamic-basal ganglia (CTBG) system is developed that reproduces key clinical features of Parkinson's disease, including its characteristic 4-8 Hz and 13-30 Hz electrophysiological signatures. Deep brain stimulation of the STN is then modeled and shown to suppress the pathological 13-30 Hz (beta) activity for physiologically realistic and optimized stimulus parameters. This supports the idea that suppression of abnormally coherent activity in the CTBG system is a major factor in DBS therapy for Parkinson's disease, by permitting normal dynamics to resume. At high stimulus intensities, nonlinear effects in the target population mediate wave-wave interactions between resonant beta activity and the stimulus pulse train, leading to complex spectral structure that shows remarkable similarity to that seen in steady-state evoked potential experiments.

Robust and tunable bursting requires slow positive feedback

We highlight that the robustness and tunability of a bursting model critically rely on currents that provide slow positive feedback to the membrane potential. Such currents have the ability to make the total conductance of the circuit negative in a timescale that is termed "slow" because it is intermediate between the fast timescale of the spike upstroke and the ultraslow timescale of even slower adaptation currents. We discuss how such currents can be assessed either in voltage-clamp experiments or in computational models. We show that, while frequent in the literature, mathematical and computational models of bursting that lack the slow negative conductance are fragile and rigid. Our results suggest that modeling the slow negative conductance of cellular models is important when studying the neuromodulation of rhythmic circuits at any broader scale. NEW & NOTEWORTHY Nervous system functions rely on the modulation of neuronal activity between different rhythmic patterns. The mechanisms of this modulation are still poorly understood. Using computational modeling, we show the critical role of currents that provide slow negative conductance, distinct from the fast negative conductance necessary for spike generation. The significance of the slow negative conductance for neuromodulation is often overlooked, leading to computational models that are rigid and fragile.

Intrinsic sodium currents and excitatory synaptic transmission influence spontaneous firing in up and down activities

Periodic up and down transitions of membrane potentials are considered to be a significant spontaneous activity. These kinds of oscillations always accompany with some spontaneous firing in up state. Our previous theoretical studies mainly looked at the subthreshold up and down transitions and characteristics of up and down dynamics. In this paper, we focus on suprathreshold spontaneous firing of up and down transitions based on improved network model and its stimulations. The simulated results indicate that fast sodium current is critical to the generation of spontaneous neural firing. While persistent sodium current plays a part in spontaneous fluctuation. Both intrinsic fast and persistent sodium dynamics influence spontaneous firing rate and synchronous activity in up and down behavior. Meanwhile, blocking excitatory synaptic transmission decreases neural firing and reveals spontaneous firing. These simulated results are basically in accordance with experimental results. Through the observation and analysis of the findings, we prove the validity of the model so we can further adopt this model to study other properties and characteristics of the network, laying the foundation for further work on cortex activity.

Unified neural field theory of brain dynamics underlying oscillations in Parkinson's disease and generalized epilepsies

The mechanisms underlying pathologically synchronized neural oscillations in Parkinson's disease (PD) and generalized epilepsies are explored in parallel via a physiologically-based neural field model of the corticothalamic-basal ganglia (CTBG) system. The basal ganglia (BG) are approximated as a single effective population and their roles in the modulation of oscillatory dynamics of the corticothalamic (CT) system and vice versa are analyzed. In addition to normal EEG rhythms, enhanced activity around 4 Hz and 20 Hz exists in the model, consistent with the characteristic frequencies observed in PD. These rhythms result from resonances in loops formed between the BG and CT populations, analogous to those that underlie epileptic oscillations in a previous CT model, and which are still present in the combined CTBG system. Dopamine depletion is argued to weaken the dampening of these loop resonances in PD, and network connections then explain the significant coherence observed between BG, thalamic, and cortical population activity around 4-8 Hz and 20 Hz. Parallels between the afferent and efferent connection sites of the thalamic reticular nucleus (TRN) and BG predict low dopamine to correspond to a reduced likelihood of tonic-clonic (grand mal) seizures, which agrees with experimental findings. Furthermore, the model predicts an increased likelihood of absence (petit mal) seizure resulting from pathologically low dopamine levels in accordance with experimental observations. Suppression of absence seizure activity is demonstrated when afferent and efferent BG connections to the CT system are strengthened, which is consistent with other CTBG modeling studies. The BG are demonstrated to have a suppressive effect on activity of the CTBG system near tonic-clonic seizure states, which provides insight into the reported efficacy of current treatments in BG circuits. Sleep states of the TRN are also found to suppress pathological PD activity in accordance with observations. Overall, the findings demonstrate strong parallels between coherent oscillations in generalized epilepsies and PD, and provide insights into possible comorbidities.

Individual brain structure and modelling predict seizure propagation

See Lytton (doi:10.1093/awx018) for a scientific commentary on this article.Neural network oscillations are a fundamental mechanism for cognition, perception and consciousness. Consequently, perturbations of network activity play an important role in the pathophysiology of brain disorders. When structural information from non-invasive brain imaging is merged with mathematical modelling, then generative brain network models constitute personalized in silico platforms for the exploration of causal mechanisms of brain function and clinical hypothesis testing. We here demonstrate with the example of drug-resistant epilepsy that patient-specific virtual brain models derived from diffusion magnetic resonance imaging have sufficient predictive power to improve diagnosis and surgery outcome. In partial epilepsy, seizures originate in a local network, the so-called epileptogenic zone, before recruiting other close or distant brain regions. We create personalized large-scale brain networks for 15 patients and simulate the individual seizure propagation patterns. Model validation is performed against the presurgical stereotactic electroencephalography data and the standard-of-care clinical evaluation. We demonstrate that the individual brain models account for the patient seizure propagation patterns, explain the variability in postsurgical success, but do not reliably augment with the use of patient-specific connectivity. Our results show that connectome-based brain network models have the capacity to explain changes in the organization of brain activity as observed in some brain disorders, thus opening up avenues towards discovery of novel clinical interventions.

State-Dependent Modulation of Slow Wave Motifs towards Awakening

Slow cortical waves that propagate across the cerebral cortex forming large-scale spatiotemporal propagation patterns are a hallmark of non-REM sleep and anesthesia, but also occur during resting wakefulness. To investigate how the spatial temporal properties of slow waves change with the depth of anesthetic, we optically imaged population voltage transients generated by mouse layer 2/3 pyramidal neurons across one or two cortical hemispheres dorsally with a genetically encoded voltage indicator (GEVI). From deep barbiturate anesthesia to light barbiturate sedation, depolarizing wave events recruiting at least 50% of the imaged cortical area consistently appeared as a conserved repertoire of distinct wave motifs. Toward awakening, the incidence of individual motifs changed systematically (the motif propagating from visual to motor areas increased while that from somatosensory to visual areas decreased) and both local and global cortical dynamics accelerated. These findings highlight that functional endogenous interactions between distant cortical areas are not only constrained by anatomical connectivity, but can also be modulated by the brain state.

Phase Difference between Model Cortical Areas Determines Level of Information Transfer

Communication between cortical sites is mediated by long-range synaptic connections. However, these connections are relatively static, while everyday cognitive tasks demand a fast and flexible routing of information in the brain. Synchronization of activity between distant cortical sites has been proposed as the mechanism underlying such a dynamic communication structure. Here, we study how oscillatory activity affects the excitability and input-output relation of local cortical circuits and how it alters the transmission of information between cortical circuits. To this end, we develop model circuits showing fast oscillations by the PING mechanism, of which the oscillatory characteristics can be altered. We identify conditions for synchronization between two brain circuits and show that the level of intercircuit coherence and the phase difference is set by the frequency difference between the intrinsic oscillations. We show that the susceptibility of the circuits to inputs, i.e., the degree of change in circuit output following input pulses, is not uniform throughout the oscillation period and that both firing rate, frequency and power are differentially modulated by inputs arriving at different phases. As a result, an appropriate phase difference between the circuits is critical for the susceptibility windows of the circuits in the network to align and for information to be efficiently transferred. We demonstrate that changes in synchrony and phase difference can be used to set up or abolish information transfer in a network of cortical circuits.

Speed hysteresis and noise shaping of traveling fronts in neural fields: role of local circuitry and nonlocal connectivity

Neural field models are powerful tools to investigate the richness of spatiotemporal activity patterns like waves and bumps, emerging from the cerebral cortex. Understanding how spontaneous and evoked activity is related to the structure of underlying networks is of central interest to unfold how information is processed by these systems. Here we focus on the interplay between local properties like input-output gain function and recurrent synaptic self-excitation of cortical modules, and nonlocal intermodular synaptic couplings yielding to define a multiscale neural field. In this framework, we work out analytic expressions for the wave speed and the stochastic diffusion of propagating fronts uncovering the existence of an optimal balance between local and nonlocal connectivity which minimizes the fluctuations of the activation front propagation. Incorporating an activity-dependent adaptation of local excitability further highlights the independent role that local and nonlocal connectivity play in modulating the speed of propagation of the activation and silencing wavefronts, respectively. Inhomogeneities in space of local excitability give raise to a novel hysteresis phenomenon such that the speed of waves traveling in opposite directions display different velocities in the same location. Taken together these results provide insights on the multiscale organization of brain slow-waves measured during deep sleep and anesthesia.

Long-range synchrony and emergence of neural reentry

Neural synchronization across long distances is a functionally important phenomenon in health and disease. In order to access the basis of different modes of long-range synchrony, we monitor spiking activities over centimetre scale in cortical networks and show that the mode of synchrony depends upon a length scale, λ, which is the minimal path that activity should propagate through to find its point of origin ready for reactivation. When λ is larger than the physical dimension of the network, distant neuronal populations operate synchronously, giving rise to irregularly occurring network-wide events that last hundreds of milliseconds to several seconds. In contrast, when λ approaches the dimension of the network, a continuous self-sustained reentry propagation emerges, a regular seizure-like mode that is marked by precise spatiotemporal patterns ('synfire chains') and may last many minutes. Termination of a reentry phase is preceded by a decrease of propagation speed to a halt. Stimulation decreases both propagation speed and λ values, which modifies the synchrony mode respectively. The results contribute to the understanding of the origin and termination of different modes of neural synchrony as well as their long-range spatial patterns, while hopefully catering to manipulation of the phenomena in pathological conditions.

Physiological expression of olfactory discrimination rule learning balances whole-population modulation and circuit stability in the piriform cortex network

Once trained, rats are able to execute particularly difficult olfactory discrimination tasks with exceptional accuracy. Such skill acquisition, termed "rule learning", is accompanied by a series of long-lasting modifications to three cellular properties which modulate pyramidal neuron activity in piriform cortex; intrinsic excitability, synaptic excitation, and synaptic inhibition. Here, we explore how these changes, which are seemingly contradictory at the single-cell level in terms of their effect on neuronal excitation, are manifested within the piriform cortical neuronal network to store the memory of the rule, while maintaining network stability. To this end, we monitored network activity via multisite extracellular recordings of field postsynaptic potentials (fPSPS) and with single-cell recordings of miniature inhibitory and excitatory synaptic events in piriform cortex slices. We show that although 5 days after rule learning the cortical network maintains its basic activity patterns, synaptic connectivity is strengthened specifically between spatially proximal cells. Moreover, while the enhancement of inhibitory and excitatory synaptic connectivity is nearly identical, strengthening of synaptic inhibition is equally distributed between neurons while synaptic excitation is particularly strengthened within a specific subgroup of cells. We suggest that memory for the acquired rule is stored mainly by strengthening excitatory synaptic connection between close pyramidal neurons and runaway synaptic activity arising from this change is prevented by a nonspecific enhancement of synaptic inhibition.

Voltage imaging to understand connections and functions of neuronal circuits

Understanding of the cellular mechanisms underlying brain functions such as cognition and emotions requires monitoring of membrane voltage at the cellular, circuit, and system levels. Seminal voltage-sensitive dye and calcium-sensitive dye imaging studies have demonstrated parallel detection of electrical activity across populations of interconnected neurons in a variety of preparations. A game-changing advance made in recent years has been the conceptualization and development of optogenetic tools, including genetically encoded indicators of voltage (GEVIs) or calcium (GECIs) and genetically encoded light-gated ion channels (actuators, e.g., channelrhodopsin2). Compared with low-molecular-weight calcium and voltage indicators (dyes), the optogenetic imaging approaches are 1) cell type specific, 2) less invasive, 3) able to relate activity and anatomy, and 4) facilitate long-term recordings of individual cells' activities over weeks, thereby allowing direct monitoring of the emergence of learned behaviors and underlying circuit mechanisms. We highlight the potential of novel approaches based on GEVIs and compare those to calcium imaging approaches. We also discuss how novel approaches based on GEVIs (and GECIs) coupled with genetically encoded actuators will promote progress in our knowledge of brain circuits and systems.

Laminar Neural Field Model of Laterally Propagating Waves of Orientation Selectivity

We construct a laminar neural-field model of primary visual cortex (V1) consisting of a superficial layer of neurons that encode the spatial location and orientation of a local visual stimulus coupled to a deep layer of neurons that only encode spatial location. The spatially-structured connections in the deep layer support the propagation of a traveling front, which then drives propagating orientation-dependent activity in the superficial layer. Using a combination of mathematical analysis and numerical simulations, we establish that the existence of a coherent orientation-selective wave relies on the presence of weak, long-range connections in the superficial layer that couple cells of similar orientation preference. Moreover, the wave persists in the presence of feedback from the superficial layer to the deep layer. Our results are consistent with recent experimental studies that indicate that deep and superficial layers work in tandem to determine the patterns of cortical activity observed in vivo.

Scale-Free Navigational Planning by Neuronal Traveling Waves

Spatial navigation and planning is assumed to involve a cognitive map for evaluating trajectories towards a goal. How such a map is realized in neuronal terms, however, remains elusive. Here we describe a simple and noise-robust neuronal implementation of a path finding algorithm in complex environments. We consider a neuronal map of the environment that supports a traveling wave spreading out from the goal location opposite to direction of the physical movement. At each position of the map, the smallest firing phase between adjacent neurons indicate the shortest direction towards the goal. In contrast to diffusion or single-wave-fronts, local phase differences build up in time at arbitrary distances from the goal, providing a minimal and robust directional information throughout the map. The time needed to reach the steady state represents an estimate of an agent’s waiting time before it heads off to the goal. Given typical waiting times we estimate the minimal number of neurons involved in the cognitive map. In the context of the planning model, forward and backward spread of neuronal activity, oscillatory waves, and phase precession get a functional interpretation, allowing for speculations about the biological counterpart.

Differential effects of conductances on the phase resetting curve of a bursting neuronal oscillator

The intrinsically oscillating neurons in the crustacean pyloric circuit have membrane conductances that influence their spontaneous activity patterns and responses to synaptic activity. The relationship between the magnitudes of these membrane conductances and the response of the oscillating neurons to synaptic input has not yet been fully or systematically explored. We examined this relationship using the phase resetting curve (PRC), which summarizes the change in the cycle period of a neuronal oscillator as a function of the input's timing within the oscillation. We first utilized a large database of single-compartment model neurons to determine the effect of individual membrane conductances on PRC shape; we found that the effects vary across conductance space, but on average, the hyperpolarization-activated and leak conductances advance the PRC. We next investigated how membrane conductances affect PRCs of the isolated pacemaker kernel in the pyloric circuit of Cancer borealis by: (1) tabulating PRCs while using dynamic clamp to artificially add varying levels of specific conductances, and (2) tabulating PRCs before and after blocking the endogenous hyperpolarization-activated current. We additionally used a previously described four-compartment model to determine how the location of the hyperpolarization-activated conductance influences that current's effect on the PRC. We report that while dynamic-clamp-injected leak current has much smaller effects on the PRC than suggested by the single-compartment model, an increase in the hyperpolarization-activated conductance both advances and reduces the noisiness of the PRC in the pacemaker kernel of the pyloric circuit in both modeling and experimental studies.

Continuous neural network with windowed Hebbian learning

We introduce an extension of the classical neural field equation where the dynamics of the synaptic kernel satisfies the standard Hebbian type of learning (synaptic plasticity). Here, a continuous network in which changes in the weight kernel occurs in a specified time window is considered. A novelty of this model is that it admits synaptic weight decrease as well as the usual weight increase resulting from correlated activity. The resulting equation leads to a delay-type rate model for which the existence and stability of solutions such as the rest state, bumps, and traveling fronts are investigated. Some relations between the length of the time window and the bump width is derived. In addition, the effect of the delay parameter on the stability of solutions is shown. Also numerical simulations for solutions and their stability are presented.

A biologically constrained, mathematical model of cortical wave propagation preceding seizure termination

Epilepsy--the condition of recurrent, unprovoked seizures--manifests in brain voltage activity with characteristic spatiotemporal patterns. These patterns include stereotyped semi-rhythmic activity produced by aggregate neuronal populations, and organized spatiotemporal phenomena, including waves. To assess these spatiotemporal patterns, we develop a mathematical model consistent with the observed neuronal population activity and determine analytically the parameter configurations that support traveling wave solutions. We then utilize high-density local field potential data recorded in vivo from human cortex preceding seizure termination from three patients to constrain the model parameters, and propose basic mechanisms that contribute to the observed traveling waves. We conclude that a relatively simple and abstract mathematical model consisting of localized interactions between excitatory cells with slow adaptation captures the quantitative features of wave propagation observed in the human local field potential preceding seizure termination.

Permittivity coupling across brain regions determines seizure recruitment in partial epilepsy

Brain regions generating seizures in patients with refractory partial epilepsy are referred to as the epileptogenic zone (EZ). During a seizure, paroxysmal activity is not restricted to the EZ, but may recruit other brain regions and propagate activity through large brain networks, which comprise brain regions that are not necessarily epileptogenic. The identification of the EZ is crucial for candidates for neurosurgery and requires unambiguous criteria that evaluate the degree of epileptogenicity of brain regions. To obtain such criteria and investigate the mechanisms of seizure recruitment and propagation, we develop a mathematical framework of coupled neural populations, which can interact via signaling through a slow permittivity variable. The permittivity variable captures effects evolving on slow timescales, including extracellular ionic concentrations and energy metabolism, with time delays of up to seconds as observed clinically. Our analyses provide a set of indices quantifying the degree of epileptogenicity and predict conditions, under which seizures propagate to nonepileptogenic brain regions, explaining the responses to intracerebral electric stimulation in epileptogenic and nonepileptogenic areas. In conjunction, our results provide guidance in the presurgical evaluation of epileptogenicity based on electrographic signatures in intracerebral electroencephalograms.

Changes of Firing Rate Induced by Changes of Phase Response Curve in Bifurcation Transitions

We study dynamical mechanisms responsible for changes of the firing rate during four different bifurcation transitions in the two-dimensional Hindmarsh-Rose (2DHR) neuron model: the saddle node on an invariant circle (SNIC) bifurcation to the supercritical Andronov-Hopf (AH) one, the SNIC bifurcation to the saddle-separatrix loop (SSL) one, the AH bifurcation to the subcritical AH (SAH) one, and the SSL bifurcation to the AH one. For this purpose, we study slopes of the firing rate curve with respect to not only an external input current but also temperature that can be interpreted as a timescale in the 2DHR neuron model. These slopes are mathematically formulated with phase response curves (PRCs), expanding the firing rate with perturbations of the temperature and external input current on the one-dimensional space of the phase [Formula: see text] in the 2DHR oscillator. By analyzing the two different slopes of the firing rate curve with respect to the temperature and external input current, we find that during changes of the firing rate in all of the bifurcation transitions, the calculated slope with respect to the temperature also changes. This is largely dependent on changes in the PRC size that is also related to the slope with respect to the external input current. Furthermore, we find phase transition–like switches of the firing rate with a possible increase of the temperature during the SSL-to-AH bifurcation transition.

Synchronization of isolated downstates (K-complexes) may be caused by cortically-induced disruption of thalamic spindling

Sleep spindles and K-complexes (KCs) define stage 2 NREM sleep (N2) in humans. We recently showed that KCs are isolated downstates characterized by widespread cortical silence. We demonstrate here that KCs can be quasi-synchronous across scalp EEG and across much of the cortex using electrocorticography (ECOG) and localized transcortical recordings (bipolar SEEG). We examine the mechanism of synchronous KC production by creating the first conductance based thalamocortical network model of N2 sleep to generate both spontaneous spindles and KCs. Spontaneous KCs are only observed when the model includes diffuse projections from restricted prefrontal areas to the thalamic reticular nucleus (RE), consistent with recent anatomical findings in rhesus monkeys. Modeled KCs begin with a spontaneous focal depolarization of the prefrontal neurons, followed by depolarization of the RE. Surprisingly, the RE depolarization leads to decreased firing due to disrupted spindling, which in turn is due to depolarization-induced inactivation of the low-threshold Ca²⁺ current (I_T). Further, although the RE inhibits thalamocortical (TC) neurons, decreased RE firing causes decreased TC cell firing, again because of disrupted spindling. The resulting abrupt removal of excitatory input to cortical pyramidal neurons then leads to the downstate. Empirically, KCs may also be evoked by sensory stimuli while maintaining sleep. We reproduce this phenomenon in the model by depolarization of either the RE or the widely-projecting prefrontal neurons. Again, disruption of thalamic spindling plays a key role. Higher levels of RE stimulation also cause downstates, but by directly inhibiting the TC neurons. SEEG recordings from the thalamus and cortex in a single patient demonstrated the model prediction that thalamic spindling significantly decreases before KC onset. In conclusion, we show empirically that KCs can be widespread quasi-synchronous cortical downstates, and demonstrate with the first model of stage 2 NREM sleep a possible mechanism whereby this widespread synchrony may arise.

EEG in the most common stage of human sleep is dominated by K-complexes (KCs) and sleep spindles (bursts of 10–14 Hz oscillations) occupying the thalamus and cortex. Recently, we discovered that KCs are brief moments when the cortex becomes almost completely silent. Here, using recordings directly from the cortex of epileptic patients, we show that KCs can be quasi-synchronous across widespread cortical areas, and ask what mechanism could produce such a phenomenon. We created the first network model of realistic cortical and thalamic neurons, which spontaneously generate KCs as well as sleep spindles. We showed that the membrane channels in the reticular nucleus of the thalamus can be inactivated by excitatory inputs from the cortex, and this disrupts the spindle-generating network, which can trigger widespread cortical silence. The model prediction that thalamic spindle disruption occurs prior to KC was then observed in simultaneous recordings from the human thalamus and cortex. Understanding the cellular and network mechanisms whereby KCs arise is crucial to understanding its roles in maintaining sleep and consolidating memories.

Learning-induced modulation of the GABAB-mediated inhibitory synaptic transmission: mechanisms and functional significance

Complex olfactory-discrimination (OD) learning results in a series of intrinsic and excitatory synaptic modifications in piriform cortex pyramidal neurons that enhance the circuit excitability. Such overexcitation must be balanced to prevent runway activity while maintaining the efficient ability to store memories. We showed previously that OD learning is accompanied by enhancement of the GABAA-mediated inhibition. Here we show that GABAB-mediated inhibition is also enhanced after learning and study the mechanism underlying such enhancement and explore its functional role. We show that presynaptic, GABAB-mediated synaptic inhibition is enhanced after learning. In contrast, the population-average postsynaptic GABAB-mediated synaptic inhibition is unchanged, but its standard deviation is enhanced. Learning-induced reduction in paired pulse facilitation in the glutamatergic synapses interconnecting pyramidal neurons was abolished by application of the GABAB antagonist CGP55845 but not by blocking G protein-gated inwardly rectifying potassium channels only, indicating enhanced suppression of excitatory synaptic release via presynaptic GABAB-receptor activation. In addition, the correlation between the strengths of the early (GABAA-mediated) and late (GABAB-mediated) synaptic inhibition was much stronger for each particular neuron after learning. Consequently, GABAB-mediated inhibition was also more efficient in controlling epileptic-like activity induced by blocking GABAA receptors. We suggest that complex OD learning is accompanied by enhancement of the GABAB-mediated inhibition that enables the cortical network to store memories, while preventing uncontrolled activity.

Effect of phase response curve skew on synchronization with and without conduction delays

A central problem in cortical processing including sensory binding and attentional gating is how neurons can synchronize their responses with zero or near-zero time lag. For a spontaneously firing neuron, an input from another neuron can delay or advance the next spike by different amounts depending upon the timing of the input relative to the previous spike. This information constitutes the phase response curve (PRC). We present a simple graphical method for determining the effect of PRC shape on synchronization tendencies and illustrate it using type 1 PRCs, which consist entirely of advances (delays) in response to excitation (inhibition). We obtained the following generic solutions for type 1 PRCs, which include the pulse-coupled leaky integrate and fire model. For pairs with mutual excitation, exact synchrony can be stable for strong coupling because of the stabilizing effect of the causal limit region of the PRC in which an input triggers a spike immediately upon arrival. However, synchrony is unstable for short delays, because delayed inputs arrive during a refractory period and cannot trigger an immediate spike. Right skew destabilizes antiphase and enables modes with time lags that grow as the conduction delay is increased. Therefore, right skew favors near synchrony at short conduction delays and a gradual transition between synchrony and antiphase for pairs coupled by mutual excitation. For pairs with mutual inhibition, zero time lag synchrony is stable for conduction delays ranging from zero to a substantial fraction of the period for pairs. However, for right skew there is a preferred antiphase mode at short delays. In contrast to mutual excitation, left skew destabilizes antiphase for mutual inhibition so that synchrony dominates at short delays as well. These pairwise synchronization tendencies constrain the synchronization properties of neurons embedded in larger networks.

Introduction to focus issue: rhythms and dynamic transitions in neurological disease: modeling, computation, and experiment

Rhythmic neuronal oscillations across a broad range of frequencies, as well as spatiotemporal phenomena, such as waves and bumps, have been observed in various areas of the brain and proposed as critical to brain function. While there is a long and distinguished history of studying rhythms in nerve cells and neuronal networks in healthy organisms, the association and analysis of rhythms to diseases are more recent developments. Indeed, it is now thought that certain aspects of diseases of the nervous system, such as epilepsy, schizophrenia, Parkinson's, and sleep disorders, are associated with transitions or disruptions of neurological rhythms. This focus issue brings together articles presenting modeling, computational, analytical, and experimental perspectives about rhythms and dynamic transitions between them that are associated to various diseases.

Estimating the modulatory effects of nanoparticles on neuronal circuits using computational upscaling

BACKGROUND

Beside the promising application potential of nanotechnologies in engineering, the use of nanomaterials in medicine is growing. New therapies employing innovative nanocarrier systems to increase specificity and efficacy of drug delivery schemes are already in clinical trials. However the influence of the nanoparticles themselves is still unknown in medical applications, especially for complex interactions in neural systems. The aim of this study was to investigate in vitro effects of coated silver nanoparticles (cAgNP) on the excitability of single neuronal cells and to integrate those findings into an in silico model to predict possible effects on neuronal circuits.

METHODS

We first performed patch clamp measurements to investigate the effects of nanosized silver particles, surrounded by an organic coating, on excitability of single cells. We then determined which parameters were altered by exposure to those nanoparticles using the Hodgkin-Huxley model of the sodium current. As a third step, we integrated those findings into a well-defined neuronal circuit of thalamocortical interactions to predict possible changes in network signaling due to the applied cAgNP, in silico.

RESULTS

We observed rapid suppression of sodium currents after exposure to cAgNP in our in vitro recordings. In numerical simulations of sodium currents we identified the parameters likely affected by cAgNP. We then examined the effects of such changes on the activity of networks. In silico network modeling indicated effects of local cAgNP application on firing patterns in all neurons in the circuit.

CONCLUSION

Our sodium current simulation shows that suppression of sodium currents by cAgNP results primarily by a reduction in the amplitude of the current. The network simulation shows that locally cAgNP-induced changes result in changes in network activity in the entire network, indicating that local application of cAgNP may influence the activity throughout the network.

Mechanisms of seizure propagation in 2-dimensional centre-surround recurrent networks

Understanding how seizures spread throughout the brain is an important problem in the treatment of epilepsy, especially for implantable devices that aim to avert focal seizures before they spread to, and overwhelm, the rest of the brain. This paper presents an analysis of the speed of propagation in a computational model of seizure-like activity in a 2-dimensional recurrent network of integrate-and-fire neurons containing both excitatory and inhibitory populations and having a difference of Gaussians connectivity structure, an approximation to that observed in cerebral cortex. In the same computational model network, alternative mechanisms are explored in order to simulate the range of seizure-like activity propagation speeds (0.1-100 mm/s) observed in two animal-slice-based models of epilepsy: (1) low extracellular [Formula: see text], which creates excess excitation and (2) introduction of gamma-aminobutyric acid (GABA) antagonists, which reduce inhibition. Moreover, two alternative connection topologies are considered: excitation broader than inhibition, and inhibition broader than excitation. It was found that the empirically observed range of propagation velocities can be obtained for both connection topologies. For the case of the GABA antagonist model simulation, consistent with other studies, it was found that there is an effective threshold in the degree of inhibition below which waves begin to propagate. For the case of the low extracellular [Formula: see text] model simulation, it was found that activity-dependent reductions in inhibition provide a potential explanation for the emergence of slowly propagating waves. This was simulated as a depression of inhibitory synapses, but it may also be achieved by other mechanisms. This work provides a localised network understanding of the propagation of seizures in 2-dimensional centre-surround networks that can be tested empirically.

Structure-dynamics relationships in bursting neuronal networks revealed using a prediction framework

The question of how the structure of a neuronal network affects its functionality has gained a lot of attention in neuroscience. However, the vast majority of the studies on structure-dynamics relationships consider few types of network structures and assess limited numbers of structural measures. In this in silico study, we employ a wide diversity of network topologies and search among many possibilities the aspects of structure that have the greatest effect on the network excitability. The network activity is simulated using two point-neuron models, where the neurons are activated by noisy fluctuation of the membrane potential and their connections are described by chemical synapse models, and statistics on the number and quality of the emergent network bursts are collected for each network type. We apply a prediction framework to the obtained data in order to find out the most relevant aspects of network structure. In this framework, predictors that use different sets of graph-theoretic measures are trained to estimate the activity properties, such as burst count or burst length, of the networks. The performances of these predictors are compared with each other. We show that the best performance in prediction of activity properties for networks with sharp in-degree distribution is obtained when the prediction is based on clustering coefficient. By contrast, for networks with broad in-degree distribution, the maximum eigenvalue of the connectivity graph gives the most accurate prediction. The results shown for small () networks hold with few exceptions when different neuron models, different choices of neuron population and different average degrees are applied. We confirm our conclusions using larger () networks as well. Our findings reveal the relevance of different aspects of network structure from the viewpoint of network excitability, and our integrative method could serve as a general framework for structure-dynamics studies in biosciences.

Minimum energy control for in vitro neurons

OBJECTIVE

To demonstrate the applicability of optimal control theory for designing minimum energy charge-balanced input waveforms for single periodically-firing in vitro neurons from brain slices of Long-Evans rats.

APPROACH

The method of control uses the phase model of a neuron and does not require prior knowledge of the neuron's biological details. The phase model of a neuron is a one-dimensional model that is characterized by the neuron's phase response curve (PRC), a sensitivity measure of the neuron to a stimulus applied at different points in its firing cycle. The PRC for each neuron is experimentally obtained by measuring the shift in phase due to a short-duration pulse injected into the periodically-firing neuron at various phase values. Based on the measured PRC, continuous-time, charge-balanced, minimum energy control waveforms have been designed to regulate the next firing time of the neuron upon application at the onset of an action potential.

MAIN RESULT

The designed waveforms can achieve the inter-spike-interval regulation for in vitro neurons with energy levels that are lower than those of conventional monophasic pulsatile inputs of past studies by at least an order of magnitude. They also provide the advantage of being charge-balanced. The energy efficiency of these waveforms is also shown by performing several supporting simulations that compare the performance of the designed waveforms against that of phase shuffled surrogate inputs, variants of the minimum energy waveforms obtained from suboptimal PRCs, as well as pulsatile stimuli that are applied at the point of maximum PRC. It was found that the minimum energy waveforms perform better than all other stimuli both in terms of control and in the amount of energy used. Specifically, it was seen that these charge-balanced waveforms use at least an order of magnitude less energy than conventional monophasic pulsatile stimuli.

SIGNIFICANCE

The significance of this work is that it uses concepts from the theory of optimal control and introduces a novel approach in designing minimum energy charge-balanced input waveforms for neurons that are robust to noise and implementable in electrophysiological experiments.

Neural 'Bubble' Dynamics Revisited

In this paper, we revisit the work of John G Taylor on neural ‘bubble’ dynamics in two-dimensional neural field models. This builds on original work of Amari in a one-dimensional setting and makes use of the fact that mathematical treatments are much simpler when the firing rate function is chosen to be a Heaviside. In this case, the dynamics of an excited or active region, defining a ‘bubble’, reduce to the dynamics of the boundary. The focus of John’s work was on the properties of radially symmetric ‘bubbles’, including existence and radial stability, with applications to the theory of topographic map formation in self-organising neural networks. As well as reviewing John’s work in this area, we also include some recent results that treat more general classes of perturbations.