Shortest Loops are Pacemakers in Random Networks of Electrically Coupled Axons

Conductance-based models and the fragmentation problem: A case study based on hippocampal CA1 pyramidal cell models and epilepsy

Epilepsy has been a central topic in computational neuroscience, and in silico models have shown to be excellent tools to integrate and evaluate findings from animal and clinical settings. Among the different languages and tools for computational modeling development, NEURON stands out as one of the most used and mature neurosimulators. However, despite the vast quantity of models developed with NEURON, a fragmentation problem is evident in the great majority of models related to the same type of cell or cell properties. This fragmentation causes a lack of interoperability between the models because of differences in parameters. The problem is not related to the neurosimulator, which is prepared to reuse elements of other models, but related to decisions made during the model development, when it is not uncommon to adjust parameter values according to the necessities of the study. Here, this problem is presented by studying computational models related to temporal lobe epilepsy and the definitions of hippocampal CA1 pyramidal cells. The current assessment aims to highlight the implications of fragmentation for reliable modeling and the need to adopt a framework that allows a better interoperability between different models. This article is part of the Special Issue "NEWroscience 2018".

Postoperative seizure outcome-guided machine learning for interictal electrocorticography in neocortical epilepsy

The objective of this study was to introduce a new machine learning guided by outcome of resective epilepsy surgery defined as the presence/absence of seizures to improve data mining for interictal pathological activities in neocortical epilepsy. Electrocorticographies for 39 patients with medically intractable neocortical epilepsy were analyzed. We separately analyzed 38 frequencies from 0.9 to 800 Hz including both high-frequency activities and low-frequency activities to select bands related to seizure outcome. An automatic detector using amplitude-duration-number thresholds was used. Interictal electrocorticography data sets of 8 min for each patient were selected. In the first training data set of 20 patients, the automatic detector was optimized to best differentiate the seizure-free group from not-seizure-free-group based on ranks of resection percentages of activities detected using a genetic algorithm. The optimization was validated in a different data set of 19 patients. There were 16 (41%) seizure-free patients. The mean follow-up duration was 21 ± 11 mo (range, 13-44 mo). After validation, frequencies significantly related to seizure outcome were 5.8, 8.4-25, 30, 36, 52, and 75 among low-frequency activities and 108 and 800 Hz among high-frequency activities. Resection for 5.8, 8.4-25, 108, and 800 Hz activities consistently improved seizure outcome. Resection effects of 17-36, 52, and 75 Hz activities on seizure outcome were variable according to thresholds. We developed and validated an automated detector for monitoring interictal pathological and inhibitory/physiological activities in neocortical epilepsy using a data-driven approach through outcome-guided machine learning. NEW & NOTEWORTHY Outcome-guided machine learning based on seizure outcome was used to improve detections for interictal electrocorticographic low- and high-frequency activities. This method resulted in better separation of seizure outcome groups than others reported in the literature. The automatic detector can be trained without human intervention and no prior information. It is based only on objective seizure outcome data without relying on an expert's manual annotations. Using the method, we could find and characterize pathological and inhibitory activities.

Toward a theory of coactivation patterns in excitable neural networks

The relationship between the structural connectivity (SC) and functional connectivity (FC) of neural systems is of central importance in brain network science. It is an open question, however, how the SC-FC relationship depends on specific topological features of brain networks or the models used for describing neural dynamics. Using a basic but general model of discrete excitable units that follow a susceptible—excited—refractory activity cycle (SER model), we here analyze how the network activity patterns underlying functional connectivity are shaped by the characteristic topological features of the network. We develop an analytical framework for describing the contribution of essential topological elements, such as common inputs and pacemakers, to the coactivation of nodes, and demonstrate the validity of the approach by comparison of the analytical predictions with numerical simulations of various exemplar networks. The present analytic framework may serve as an initial step for the mechanistic understanding of the contributions of brain network topology to brain dynamics.

Functional connectivity, as reflected in the statistical dependencies of distributed activity, is widely used to probe the organization of complex systems such as the brain. While this measure has been helpful for characterizing brain states and highlighting alterations of brain dynamics in various diseases, the mechanisms underlying the generation of FC patterns remain poorly understood. One prominent factor shaping FC is the underlying neural network structure. Using a minimalist model of excitation, we investigate how the topology of excitable neural networks contributes to FC. Specifically, we show that FC can be analytically predicted from the way in which the nodes are embedded in the network and how they are related to basic self-organizing units of excitable dynamics, particularly, short pacemaker cycles. These insights are a step towards a mechanistic understanding of the activation patterns of complex neural networks.

Distribution of shortest cycle lengths in random networks

We present analytical results for the distribution of shortest cycle lengths (DSCL) in random networks. The approach is based on the relation between the DSCL and the distribution of shortest path lengths (DSPL). We apply this approach to configuration model networks, for which analytical results for the DSPL were obtained before. We first calculate the fraction of nodes in the network which reside on at least one cycle. Conditioning on being on a cycle, we provide the DSCL over ensembles of configuration model networks with degree distributions which follow a Poisson distribution (Erdős-Rényi network), degenerate distribution (random regular graph), and a power-law distribution (scale-free network). The mean and variance of the DSCL are calculated. The analytical results are found to be in very good agreement with the results of computer simulations.

Connectivity and complex systems: learning from a multi-disciplinary perspective

In recent years, parallel developments in disparate disciplines have focused on what has come to be termed connectivity; a concept used in understanding and describing complex systems. Conceptualisations and operationalisations of connectivity have evolved largely within their disciplinary boundaries, yet similarities in this concept and its application among disciplines are evident. However, any implementation of the concept of connectivity carries with it both ontological and epistemological constraints, which leads us to ask if there is one type or set of approach(es) to connectivity that might be applied to all disciplines. In this review we explore four ontological and epistemological challenges in using connectivity to understand complex systems from the standpoint of widely different disciplines. These are: (i) defining the fundamental unit for the study of connectivity; (ii) separating structural connectivity from functional connectivity; (iii) understanding emergent behaviour; and (iv) measuring connectivity. We draw upon discipline-specific insights from Computational Neuroscience, Ecology, Geomorphology, Neuroscience, Social Network Science and Systems Biology to explore the use of connectivity among these disciplines. We evaluate how a connectivity-based approach has generated new understanding of structural-functional relationships that characterise complex systems and propose a 'common toolbox' underpinned by network-based approaches that can advance connectivity studies by overcoming existing constraints.

Topological determinants of self-sustained activity in a simple model of excitable dynamics on graphs

Simple models of excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This topic is of practical relevance to diverse fields, ranging from neuroscience to engineering. Here we analyze how a single excitation propagates through a random network as a function of the excitation threshold, that is, the relative amount of activity in the neighborhood required for the excitation of a node. We observe that two sharp transitions delineate a region of sustained activity. Using analytical considerations and numerical simulation, we show that these transitions originate from the presence of barriers to propagation and the excitation of topological cycles, respectively, and can be predicted from the network topology. Our findings are interpreted in the context of network reverberations and self-sustained activity in neural systems, which is a question of long-standing interest in computational neuroscience.

High-frequency brain networks undergo modular breakdown during epileptic seizures

OBJECTIVE

Cortical high-frequency oscillations (HFOs; 100-500 Hz) play a critical role in the pathogenesis of epilepsy; however, whether they represent a true epileptogenic process remains largely unknown. HFOs have been recorded in the human cortex but their network dynamics during the transitional period from interictal to ictal phase remain largely unknown. We sought to determine the high-frequency network dynamics of these oscillations in patients with epilepsy who were undergoing intracranial electroencephalographic recording for seizure localization.

METHODS

We applied a graph theoretical analysis framework to high-resolution intracranial electroencephalographic recordings of 24 interictal and 24 seizure periods to identify the spatiotemporal evolution of community structure of high-frequency cortical networks at rest and during multiple seizure episodes in patients with intractable epilepsy.

RESULTS

Cortical networks at all examined frequencies showed temporally stable community architecture in all 24 interictal periods. During seizure periods, high-frequency networks showed a significant breakdown of their community structure, which was characterized by the emergence of numerous small nodal communities, not limited to seizure foci and encompassing the entire recorded network. Such network disorganization was observed on average 225 s before the electrographic seizure onset and extended on average 190 s after termination of the seizure. Gamma networks were characterized by stable community dynamics during resting and seizure periods.

SIGNIFICANCE

Our findings suggest that the modular breakdown of high-frequency cortical networks represents a distinct functional pathology that underlies epileptogenesis and corresponds to a cortical state of highest propensity to generate seizures.

GABAA receptor-mediated feedforward and feedback inhibition differentially modulate the gain and the neural code transformation in hippocampal CA1 pyramidal cells

Diverse variety of hippocampal interneurons exists in the CA1 area, which provides either feedforward (FF) or feedback (FB) inhibition to CA1 pyramidal cell (PC). However, how the two different inhibitory network architectures modulate the computational mode of CA1 PC is unknown. By investigating the CA3 PC rate-driven input-output function of CA1 PC using in vitro electrophysiology, in vitro-simulation of inhibitory network, and in silico computational modeling, we demonstrated for the first time that GABAA receptor-mediated FF and FB inhibition differentially modulate the gain, the spike precision, the neural code transformation and the information capacity of CA1 PC. Recruitment of FF inhibition buffered the CA1 PC spikes to theta-frequency regardless of the input frequency, abolishing the gain and making CA1 PC insensitive to its inputs. Instead, temporal variability of the CA1 PC spikes was increased, promoting the rate-to-temporal code transformation to enhance the information capacity of CA1 PC. In contrast, the recruitment of FB inhibition sub-linearly transformed the input rate to spike output rate with high gain and low spike temporal variability, promoting the rate-to-rate code transformation. These results suggest that GABAA receptor-mediated FF and FB inhibitory circuits could serve as network mechanisms for differentially modulating the gain of CA1 PC, allowing CA1 PC to switch between different computational modes using rate and temporal codes ad hoc. Such switch will allow CA1 PC to efficiently respond to spatio-temporally dynamic inputs and expand its computational capacity during different behavioral and neuromodulatory states in vivo.

Role of long cycles in excitable dynamics on graphs

Topological cycles in excitable networks can play an important role in maintaining the network activity. When properly activated, cycles act as dynamic pacemakers, sustaining the activity of the whole network. Most previous research has focused on the contributions of short cycles to network dynamics. Here, we identify the specific cycles that are used during different runs of activation in sparse random graphs, as a basis of characterizing the contribution of cycles of any length. Both simulation and a refined mean-field approach evidence a decrease in the cycle usage when the cycle length increases, reflecting a trade-off between long time for recovery after excitation and low vulnerability to out-of-phase external excitations. In spite of this statistical observation, we find that the successful usage of long cycles, though rare, has important functional consequences for sustaining network activity: The average cycle length is the main feature of the cycle length distribution that affects the average lifetime of activity in the network. Particularly, use of long, rather than short, cycles correlates with higher lifetime, and cutting shortcuts in long cycles tends to increase the average lifetime of the activity. Our findings, thus, emphasize the essential, previously underrated role of long cycles in sustaining network activity. On a more general level, the findings underline the importance of network topology, particularly cycle structure, for self-sustained network dynamics.

Excitation and inhibition in recurrent networks mediate collision avoidance in Xenopus tadpoles

Information processing in the vertebrate brain is thought to be mediated through distributed neural networks, but it is still unclear how sensory stimuli are encoded and detected by these networks, and what role synaptic inhibition plays in this process. Here we used a collision avoidance behavior in Xenopus tadpoles as a model for stimulus discrimination and recognition. We showed that the visual system of the tadpole is selective for behaviorally relevant looming stimuli, and that the detection of these stimuli first occurs in the optic tectum. By comparing visually guided behavior, optic nerve recordings, excitatory and inhibitory synaptic currents, and the spike output of tectal neurons, we showed that collision detection in the tadpole relies on the emergent properties of distributed recurrent networks within the tectum. We found that synaptic inhibition was temporally correlated with excitation, and did not actively sculpt stimulus selectivity, but rather it regulated the amount of integration between direct inputs from the retina and recurrent inputs from the tectum. Both pharmacological suppression and enhancement of synaptic inhibition disrupted emergent selectivity for looming stimuli. Taken together these findings suggested that, by regulating the amount of network activity, inhibition plays a critical role in maintaining selective sensitivity to behaviorally-relevant visual stimuli.

In situ three-dimensional reconstruction of mouse heart sympathetic innervation by two-photon excitation fluorescence imaging

BACKGROUND

Sympathetic nerve wiring in the mammalian heart has remained largely unexplored. Resolving the wiring diagram of the cardiac sympathetic network would help establish the structural underpinnings of neurocardiac coupling.

NEW METHOD

We used two-photon excitation fluorescence microscopy, combined with a computer-assisted 3-D tracking algorithm, to map the local sympathetic circuits in living hearts from adult transgenic mice expressing enhanced green fluorescent protein (EGFP) in peripheral adrenergic neurons.

RESULTS

Quantitative co-localization analyses confirmed that the intramyocardial EGFP distribution recapitulated the anatomy of the sympathetic arbor. In the left ventricular subepicardium of the uninjured heart, the sympathetic network was composed of multiple subarbors, exhibiting variable branching and looping topology. Axonal branches did not overlap with each other within their respective parental subarbor nor with neurites of annexed subarbors. The sympathetic network in the border zone of a 2-week-old myocardial infarction was characterized by substantive rewiring, which included spatially heterogeneous loss and gain of sympathetic fibers and formation of multiple, predominately nested, axon loops of widely variable circumference and geometry.

COMPARISON WITH EXISTING METHODS

In contrast to mechanical tissue sectioning methods that may involve deformation of tissue and uncertainty in registration across sections, our approach preserves continuity of structure, which allows tracing of neurites over distances, and thus enables derivation of the three-dimensional and topological morphology of cardiac sympathetic nerves.

CONCLUSIONS

Our assay should be of general utility to unravel the mechanisms governing sympathetic axon spacing during development and disease.

Gap junction networks can generate both ripple-like and fast ripple-like oscillations

Fast ripples (FRs) are network oscillations, defined variously as having frequencies of > 150 to > 250 Hz, with a controversial mechanism. FRs appear to indicate a propensity of cortical tissue to originate seizures. Here, we demonstrate field oscillations, at up to 400 Hz, in spontaneously epileptic human cortical tissue in vitro, and present a network model that could explain FRs themselves, and their relation to 'ordinary' (slower) ripples. We performed network simulations with model pyramidal neurons, having axons electrically coupled. Ripples (< 250 Hz) were favored when conduction of action potentials, axon to axon, was reliable. Whereas ripple population activity was periodic, firing of individual axons varied in relative phase. A switch from ripples to FRs took place when an ectopic spike occurred in a cell coupled to another cell, itself multiply coupled to others. Propagation could then start in one direction only, a condition suitable for re-entry. The resulting oscillations were > 250 Hz, were sustained or interrupted, and had little jitter in the firing of individual axons. The form of model FR was similar to spontaneously occurring FRs in excised human epileptic tissue. In vitro, FRs were suppressed by a gap junction blocker. Our data suggest that a given network can produce ripples, FRs, or both, via gap junctions, and that FRs are favored by clusters of axonal gap junctions. If axonal gap junctions indeed occur in epileptic tissue, and are mediated by connexin 26 (recently shown to mediate coupling between immature neocortical pyramidal cells), then this prediction is testable.

Synaptic gating at axonal branches, and sharp-wave ripples with replay: a simulation study

Mechanisms of place cell replay occurring during sharp-wave ripples (SPW-Rs) remain obscure due to the fact that ripples in vitro depend on non-synaptic mechanisms, presumably via axo-axonal gap junctions between pyramidal cells. We suggest a model of in vivo SPW-Rs in which synaptic excitatory post-synaptic potentials (EPSPs) control the axonal spiking of cells in SPW-Rs: ripple activity remains hidden in the network of axonal collaterals (connected by gap junctions) due to conduction failures, unless there is a sufficient dendritic EPSP. The EPSP brings the axonal branching point to threshold, and action potentials from the collateral start to propagate to the soma and to the distal axon. The model coherently explains multiple experimental data on SPW-Rs, both in vitro and in vivo. The mechanism of synaptic gating leads to the following implication: a sequence of pyramidal cells can be replayed at ripple frequency by the superposition of subthreshold dendritic EPSPs and ripple activity in the axonal plexus. Replay is demonstrated in both forward and reverse directions. We discuss several testable predictions. In general, the mechanism of synaptic gating suggests that pyramidal cells under certain conditions can act like a transistor.

Building blocks of self-sustained activity in a simple deterministic model of excitable neural networks

Understanding the interplay of topology and dynamics of excitable neural networks is one of the major challenges in computational neuroscience. Here we employ a simple deterministic excitable model to explore how network-wide activation patterns are shaped by network architecture. Our observables are co-activation patterns, together with the average activity of the network and the periodicities in the excitation density. Our main results are: (1) the dependence of the correlation between the adjacency matrix and the instantaneous (zero time delay) co-activation matrix on global network features (clustering, modularity, scale-free degree distribution), (2) a correlation between the average activity and the amount of small cycles in the graph, and (3) a microscopic understanding of the contributions by 3-node and 4-node cycles to sustained activity.

Inhibition enhances memory capacity: optimal feedback, transient replay and oscillations

Recurring sequences of neuronal activation in the hippocampus are a candidate for a neurophysiological correlate of episodic memory. Here, we discuss a mean-field theory for such spike sequences in phase space and show how they become unstable when the neuronal network operates at maximum memory capacity. We find that inhibitory feedback rescues replay of the sequences, giving rise to oscillations and thereby enhancing the network's capacity. We further argue that transient sequences in an overloaded network with feedback inhibition may provide a mechanistic picture of memory-related neuronal activity during hippocampal sharp-wave ripple complexes.