Shortest Loops are Pacemakers in Random Networks of Electrically Coupled Axons

High-frequency oscillations (HFOs) are an important part of brain activity in health and disease. However, their origins remain obscure and controversial. One possible mechanism depends on the presence of sparsely distributed gap junctions that electrically couple the axons of principal cells. A plexus of electrically coupled axons is modeled as a random network with bi-directional connections between its nodes. Under certain conditions the network can demonstrate one of two types of oscillatory activity. Type I oscillations (100–200 Hz) are predicted to be caused by spontaneously spiking axons in a network with strong (high conductance) gap junctions. Type II oscillations (200–300 Hz) require no spontaneous spiking and relatively weak (low-conductance) gap junctions, across which spike propagation failures occur. The type II oscillations are reentrant and self-sustained. Here we examine what determines the frequency of type II oscillations. Using simulations we show that the distribution of loop lengths is the key factor for determining frequency in type II network oscillations. We first analyze spike failure between two electrically coupled cells using a model of anatomically reconstructed CA1 pyramidal neuron. Then network oscillations are studied by a cellular automaton model with random network connectivity, in which we control loop statistics. We show that oscillation periods can be predicted from the network’s loop statistics. The shortest loop, around which a spike can travel, is the most likely pacemaker candidate. The principle of one loop as a pacemaker is remarkable, because random networks contain a large number of loops juxtaposed and superimposed, and their number rapidly grows with network size. This principle allows us to predict the frequency of oscillations from network connectivity and visa versa. We finally propose that type I oscillations may correspond to ripples, while type II oscillations correspond to so-called fast ripples

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

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

New dynamics in cerebellar Purkinje cells: torus canards

We describe a transition from bursting to rapid spiking in a reduced mathematical model of a cerebellar Purkinje cell. We perform a slow-fast analysis of the system and find that -- after a saddle node bifurcation of limit cycles -- the full model dynamics follow temporarily a repelling branch of limit cycles. We propose that the system exhibits a dynamical phenomenon new to realistic, biophysical applications: torus canards.Comment: 4 pages; 4 figures (low resolution); updated following peer-review: language and definitions updated, Figures 1 and 4 updated, typos corrected, references added and remove

Period Concatenation Underlies Interactions between Gamma and Beta Rhythms in Neocortex

The neocortex generates rhythmic electrical activity over a frequency range covering many decades. Specific cognitive and motor states are associated with oscillations in discrete frequency bands within this range, but it is not known whether interactions and transitions between distinct frequencies are of functional importance. When coexpressed rhythms have frequencies that differ by a factor of two or more interactions can be seen in terms of phase synchronization. Larger frequency differences can result in interactions in the form of nesting of faster frequencies within slower ones by a process of amplitude modulation. It is not known how coexpressed rhythms, whose frequencies differ by less than a factor of two may interact. Here we show that two frequencies (gamma – 40 Hz and beta2 – 25 Hz), coexpressed in superficial and deep cortical laminae with low temporal interaction, can combine to generate a third frequency (beta1 – 15 Hz) showing strong temporal interaction. The process occurs via period concatenation, with basic rhythm-generating microcircuits underlying gamma and beta2 rhythms forming the building blocks of the beta1 rhythm by a process of addition. The mean ratio of adjacent frequency components was a constant – approximately the golden mean – which served to both minimize temporal interactions, and permit multiple transitions, between frequencies. The resulting temporal landscape may provide a framework for multiplexing – parallel information processing on multiple temporal scales

Mixed Electrical–Chemical Synapses in Adult Rat Hippocampus are Primarily Glutamatergic and Coupled by Connexin-36

Dendrodendritic electrical signaling via gap junctions is now an accepted feature of neuronal communication in mammalian brain, whereas axodendritic and axosomatic gap junctions have rarely been described. We present ultrastructural, immunocytochemical, and dye-coupling evidence for “mixed” (electrical/chemical) synapses on both principal cells and interneurons in adult rat hippocampus. Thin-section electron microscopic images of small gap junction-like appositions were found at mossy fiber (MF) terminals on thorny excrescences of CA3 pyramidal neurons (CA3pyr), apparently forming glutamatergic mixed synapses. Lucifer Yellow injected into weakly fixed CA3pyr was detected in MF axons that contacted four injected CA3pyr, supporting gap junction-mediated coupling between those two types of principal cells. Freeze-fracture replica immunogold labeling revealed diverse sizes and morphologies of connexin-36-containing gap junctions throughout hippocampus. Of 20 immunogold-labeled gap junctions, seven were large (328–1140 connexons), three of which were consistent with electrical synapses between interneurons; but nine were at axon terminal synapses, three of which were immediately adjacent to distinctive glutamate receptor-containing postsynaptic densities, forming mixed glutamatergic synapses. Four others were adjacent to small clusters of immunogold-labeled 10-nm E-face intramembrane particles, apparently representing extrasynaptic glutamate receptor particles. Gap junctions also were on spines in stratum lucidum, stratum oriens, dentate gyrus, and hilus, on both interneurons and unidentified neurons. In addition, one putative GABAergic mixed synapse was found in thin-section images of a CA3pyr, but none were found by immunogold labeling, suggesting the rarity of GABAergic mixed synapses. Cx36-containing gap junctions throughout hippocampus suggest the possibility of reciprocal modulation of electrical and chemical signals in diverse hippocampal neurons

The RING E3 ligase KEEP ON GOING modulates JASMONATE ZIM-DOMAIN12 stability

Jasmonate (JA) signaling in plants is mediated by the JASMONATE ZIM-DOMAIN (JAZ) proteins that repress the activity of several transcription factors regulating JA-inducible gene expression. The hormone JA-isoleucine triggers the interaction of JAZ repressor proteins with the F-box protein CORONATINE INSENSITIVE1 (COI1), part of an S-phase kinase-associated protein1/Cullin1/F-box protein COI1 (SCFCOI1) E3 ubiquitin ligase complex, and their degradation by the 26S proteasome. In Arabidopsis (Arabidopsis thaliana), the JAZ family consists of 13 members. The level of redundancy or specificity among these members is currently not well understood. Here, we characterized JAZ12, encoded by a highly expressed JAZ gene. JAZ12 interacted with the transcription factors MYC2, MYC3, and MYC4 in vivo and repressed MYC2 activity. Using tandem affinity purification, we found JAZ12 to interact with SCFCOI1 components, matching with observed in vivo ubiquitination and with rapid degradation after treatment with JA. In contrast to the other JAZ proteins, JAZ12 also interacted directly with the E3 RING ligase KEEP ON GOING (KEG), a known repressor of the ABSCISIC ACID INSENSITIVE5 transcription factor in abscisic acid signaling. To study the functional role of this interaction, we circumvented the lethality of keg loss-of-function mutants by silencing KEG using an artificial microRNA approach. Abscisic acid treatment promoted JAZ12 degradation, and KEG knockdown led to a decrease in JAZ12 protein levels. Correspondingly, KEG overexpression was capable of partially inhibiting COI1-mediated JAZ12 degradation. Our results provide additional evidence for KEG as an important factor in plant hormone signaling and a positive regulator of JAZ12 stability

Theta/delta coupling across cortical laminae contributes to semantic cognition

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

On the role of theory and modeling in neuroscience

In recent years, the field of neuroscience has gone through rapid experimental advances and extensive use of quantitative and computational methods. This accelerating growth has created a need for methodological analysis of the role of theory and the modeling approaches currently used in this field. Toward that end, we start from the general view that the primary role of science is to solve empirical problems, and that it does so by developing theories that can account for phenomena within their domain of application. We propose a commonly-used set of terms - descriptive, mechanistic, and normative - as methodological designations that refer to the kind of problem a theory is intended to solve. Further, we find that models of each kind play distinct roles in defining and bridging the multiple levels of abstraction necessary to account for any neuroscientific phenomenon. We then discuss how models play an important role to connect theory and experiment, and note the importance of well-defined translation functions between them. Furthermore, we describe how models themselves can be used as a form of experiment to test and develop theories. This report is the summary of a discussion initiated at the conference Present and Future Theoretical Frameworks in Neuroscience, which we hope will contribute to a much-needed discussion in the neuroscientific community

Rhythm Generation through Period Concatenation in Rat Somatosensory Cortex

Rhythmic voltage oscillations resulting from the summed activity of neuronal populations occur in many nervous systems. Contemporary observations suggest that coexistent oscillations interact and, in time, may switch in dominance. We recently reported an example of these interactions recorded from in vitro preparations of rat somatosensory cortex. We found that following an initial interval of coexistent gamma (∼25 ms period) and beta2 (∼40 ms period) rhythms in the superficial and deep cortical layers, respectively, a transition to a synchronous beta1 (∼65 ms period) rhythm in all cortical layers occurred. We proposed that the switch to beta1 activity resulted from the novel mechanism of period concatenation of the faster rhythms: gamma period (25 ms)+beta2 period (40 ms) = beta1 period (65 ms). In this article, we investigate in greater detail the fundamental mechanisms of the beta1 rhythm. To do so we describe additional in vitro experiments that constrain a biologically realistic, yet simplified, computational model of the activity. We use the model to suggest that the dynamic building blocks (or motifs) of the gamma and beta2 rhythms combine to produce a beta1 oscillation that exhibits cross-frequency interactions. Through the combined approach of in vitro experiments and mathematical modeling we isolate the specific components that promote or destroy each rhythm. We propose that mechanisms vital to establishing the beta1 oscillation include strengthened connections between a population of deep layer intrinsically bursting cells and a transition from antidromic to orthodromic spike generation in these cells. We conclude that neural activity in the superficial and deep cortical layers may temporally combine to generate a slower oscillation