Clique of functional hubs orchestrates population bursts in developmentally regulated neural networks

It has recently been discovered that single neuron stimulation can impact network dynamics in immature and adult neuronal circuits. Here we report a novel mechanism which can explain in neuronal circuits, at an early stage of development, the peculiar role played by a few specific neurons in promoting/arresting the population activity. For this purpose, we consider a standard neuronal network model, with short-term synaptic plasticity, whose population activity is characterized by bursting behavior. The addition of developmentally inspired constraints and correlations in the distribution of the neuronal connectivities and excitabilities leads to the emergence of functional hub neurons, whose stimulation/deletion is critical for the network activity. Functional hubs form a clique, where a precise sequential activation of the neurons is essential to ignite collective events without any need for a specific topological architecture. Unsupervised time-lagged firings of supra-threshold cells, in connection with coordinated entrainments of near-threshold neurons, are the key ingredients to orchestrateComment: 39 pages, 15 figures, to appear in PLOS Computational Biolog

Phase synchronization of coupled bursting neurons and the generalized Kuramoto model

Bursting neurons fire rapid sequences of action potential spikes followed by a quiescent period. The basic dynamical mechanism of bursting is the slow currents that modulate a fast spiking activity caused by rapid ionic currents. Minimal models of bursting neurons must include both effects. We considered one of these models and its relation with a generalized Kuramoto model, thanks to the definition of a geometrical phase for bursting and a corresponding frequency. We considered neuronal networks with different connection topologies and investigated the transition from a non-synchronized to a partially phase-synchronized state as the coupling strength is varied. The numerically determined critical coupling strength value for this transition to occur is compared with theoretical results valid for the generalized Kuramoto model.Comment: 31 pages, 5 figure

The Influence of Slow Calcium-Activated Potassium Channels on Epileptiform Activity in a Neuronal Model of Pyramidal Cells

An imbalance between excitation and inhibition can play an important role in the generation of epileptiform activity. Experimental evidence indicates that alterations of either synaptic activity or intrinsic membrane properties may contribute to this imbalance. The slow Ca2+ - activated K+ currents (sIAHP) limit neuronal firing rate and excitability and are therefore of great interest for their potential role in epileptogenesis. The sIAHP is found in both excitatory and inhibitory neurons, and its effect on these neurons can influence the network behavior. Simulations show that the increased excitability caused by reduction of inhibition by the sIAHP for inhibitory interneuron generates recurrent bursting activity

The Effects of Dopamine on Frequency Dependent Short Term Synaptic Plasticity: A Comparison of Layer Contributions and Rhythmic Dynamics

Executive functions (e.g. working memory [WM]) are known to be mediated by prefrontal cortical areas of the human brain which share homology with mouse medial prefrontal cortex (mPFC). Furthermore, it is well established that optimal dopaminergic input is required for proper WM function in the PFC. While it is well established that the mPFC receives inputs from several different brain areas, impinging on different compartmental regions of cells, it remains unknown how layer V pyramidal cells, the major output cells of the mPFC, integrate this information. Additionally, it remains unknown how dopamine modulates this integration by way of separate afferents and compartments within the PFC. A subset of studies presented here focus attention on the excitatory synaptic responses of layer V cells in response to compartmentalized stimulation (i.e. within the somatic region [layer V] or within the apical tufts [layer I]). Overall, these data suggest that dopamine, through D1 receptor (R) activation promotes local connectivity (primarily layer V to layer V connections) in the somatic region, while simultaneously inhibiting synaptic plasticity within the apical tufts through the suppression of NMDAR-mediated responses. Additionally, D2R activation had no effect on local layer V connectivity, but may play a role in regulating the signal-to-noise ratio in the apical tufts, by inhibiting low-frequency inputs and promoting inputs firing at high frequencies. Taken together, these results suggest that in the presence of normal dopamine levels local influences (i.e. environmental / bottom-up ) and plasticity will be promoted within layer V, while top-down\u22 or contextual information impinging on layer I is stabilized. Additional studies presented here focus attention on the excitatory synaptic responses, and modulation of dopamine, of layer V pyramids in response to inputs from the contralateral mPFC. These data suggest that D1R modulation enhances the ability of layer V cells to integrate information from the contralateral mPFC. In combination, these experiments provide insight into how normal dopaminergic receptor activation alters signal processing and integration properties of layer V cells within the mPFC and shed light on cellular mechanism disruptions in schizophrenia, a disorder characterized by dopaminergic dysregulation

A simulation study on the effects of dendritic morphology on layer V prefrontal pyramidal cell firing behaviour

Pyramidal cells, the most abundant neurons in neocortex, exhibit significant structural variability across different brain areas and layers in different species. Moreover, in response to a somatic step current, these cells display a range of firing behaviors, the most common being (1) repetitive action potentials (Regular Spiking—RS), and (2) an initial cluster of 2–5 action potentials with short interspike interval (ISIs) followed by single spikes (Intrinsic Bursting—IB). A correlation between firing behavior and dendritic morphology has recently been reported. In this work we use computational modeling to investigate quantitatively the effects of the basal dendritic tree morphology on the firing behavior of 112 three-dimensional reconstructions of layer V PFC rat pyramidal cells. Particularly, we focus on how different morphological (diameter, total length, volume, and branch number) and passive [Mean Electrotonic Path length (MEP)] features of basal dendritic trees shape somatic firing when the spatial distribution of ionic mechanisms in the basal dendritic trees is uniform or non-uniform. Our results suggest that total length, volume and branch number are the best morphological parameters to discriminate the cells as RS or IB, regardless of the distribution of ionic mechanisms in basal trees. The discriminatory power of total length, volume, and branch number remains high in the presence of different apical dendrites. These results suggest that morphological variations in the basal dendritic trees of layer V pyramidal neurons in the PFC influence their firing patterns in a predictive manner and may in turn influence the information processing capabilities of these neurons

Interacting Mechanisms Driving Synchrony in Neural Networks with Inhibitory Interneurons

Computational neuroscience contributes to our understanding of the brain by applying techniques from fields including mathematics, physics, and computer science to neuroscientific problems that are not amenable to purely biologic study. One area in which this interdisciplinary research is particularly valuable is the proposal and analysis of mechanisms underlying neural network behaviors. Neural synchrony, especially when driven by inhibitory interneurons, is a behavior of particular importance considering this behavior play a role in neural oscillations underlying important brain functions such as memory formation and attention. Typically, these oscillations arise from synchronous firing of a neural population, and thus the study of neural oscillations and neural synchrony are deeply intertwined. Such network behaviors are particularly amenable to computational analysis given the variety of mathematical techniques that are of use in this field. Inhibitory interneurons are thought to drive synchrony in ways described by two computational mechanisms: Interneuron Network Gamma (ING), which describes how an inhibitory network synchronizes itself; and Pyramidal Interneuron Network Gamma (PING), which describes how a population of interneurons inter-connected with a population of excitatory pyramidal cells (an E-I network) synchronizes both populations. As first articulated using simplified interneuron models, these mechanisms find network properties are the primary impetus for synchrony. However, as neurobiologists uncover interneurons exhibiting a vast array of cellular and intra-connectivity properties, our understanding of how interneurons drive oscillations must account for this diversity. This necessitates an investigation of how changing interneuron properties might disrupt the predictions of ING and PING, and whether other mechanisms might interact with or disrupt these network-driven mechanisms. In my dissertation, I broach this topic utilizing the Type I and Type II neuron classifications, which refer to properties derived from the mathematics of coupled oscillators. Classic ING and PING literature typically utilize Type I neurons which always respond to an excitatory perturbation with an advance of the subsequent action potential. However, many interneurons exhibit Type II properties, which respond to some excitatory perturbations with a delay in the subsequent action potential. Interneuronal diversity is also reflected in the strength and density of the synaptic connections between these neurons, which is also explored in this work. My research reveals a variety of ways in which interneuronal diversity alters synchronous oscillations in networks containing inhibitory interneurons and the mechanisms likely driving these dynamics. For example, oscillations in networks of Type II interneurons violate ING predictions and can be explained mechanistically primarily utilizing cellular properties. Additionally, varying the type of both excitatory and inhibitory cells in E-I networks reveals that synchronous excitatory activity arises with different network connectivities for different neuron types, sometimes driven by cellular properties rather than PING. Furthermore, E-I networks respond differently to varied strengths of inhibitory intra-connectivity depending upon interneuron type, sometimes in ways not fully accounted for by PING theory. Taken together, this research reveals that network-driven and cellularly-driven mechanisms promoting oscillatory activity in networks containing inhibitory interneurons interact, and oftentimes compete, in order to dictate the overall network dynamics. These dynamics are more complex than those predicted by the classic ING and PING mechanisms alone. The diverse dynamical properties imparted to oscillating neural networks by changing inhibitory interneuron properties provides some insight into the biological need for such variability.PHDApplied and Interdisciplinary MathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143981/1/sbrich_1.pd

Inhibition Modifies the Effects of Slow Calcium-Activated Potassium Channels on Epileptiform Activity in a Neuronal Network Model

Generation of epileptiform activity typically results from a change in the balance between network excitation and inhibition. Experimental evidence indicates that alterations of either synaptic activity or intrinsic membrane properties can produce increased network excitation. The slow Ca2+-activated K+ currents (sI AHP) are important modulators of neuronal firing rate and excitability and have important established and potential roles in epileptogenesis. While the effects of changes in sI AHP on individual neuronal excitability are readily studied and well established, the effects of such changes on network behavior are less well known. The experiments here utilize a defined small network model of multicompartment pyramidal cells and an inhibitory interneuron to study the effects of changes in sI AHP on network behavior. The benefits of this model system include the ability to observe activity in all cells in a network and the effects of interactions of multiple simultaneous influences. In the model with no inhibitory interneuron, increasing sI AHP results in progressively decreasing burst activity. Adding an inhibitory interneuron changes the observed effects; at modest inhibitory strengths, increasing sI AHP in all network neurons actually results in increased network bursting (except at very high values). The duration of the burst activity is influenced by the length of delay in a feedback loop, with longer loops resulting in more prolonged bursting. These observations illustrate that the study of potential antiepileptogenic membrane effects must be extended to realistic networks. Network inhibition can dramatically alter the observations seen in pure excitatory networks

Improving Associative Memory in a Network of Spiking Neurons

In this thesis we use computational neural network models to examine the dynamics and functionality of the CA3 region of the mammalian hippocampus. The emphasis of the project is to investigate how the dynamic control structures provided by inhibitory circuitry and cellular modification may effect the CA3 region during the recall of previously stored information. The CA3 region is commonly thought to work as a recurrent auto-associative neural network due to the neurophysiological characteristics found, such as, recurrent collaterals, strong and sparse synapses from external inputs and plasticity between coactive cells. Associative memory models have been developed using various configurations of mathematical artificial neural networks which were first developed over 40 years ago. Within these models we can store information via changes in the strength of connections between simplified model neurons (two-state). These memories can be recalled when a cue (noisy or partial) is instantiated upon the net. The type of information they can store is quite limited due to restrictions caused by the simplicity of the hard-limiting nodes which are commonly associated with a binary activation threshold. We build a much more biologically plausible model with complex spiking cell models and with realistic synaptic properties between cells. This model is based upon some of the many details we now know of the neuronal circuitry of the CA3 region. We implemented the model in computer software using Neuron and Matlab and tested it by running simulations of storage and recall in the network. By building this model we gain new insights into how different types of neurons, and the complex circuits they form, actually work. The mammalian brain consists of complex resistive-capacative electrical circuitry which is formed by the interconnection of large numbers of neurons. A principal cell type is the pyramidal cell within the cortex, which is the main information processor in our neural networks. Pyramidal cells are surrounded by diverse populations of interneurons which have proportionally smaller numbers compared to the pyramidal cells and these form connections with pyramidal cells and other inhibitory cells. By building detailed computational models of recurrent neural circuitry we explore how these microcircuits of interneurons control the flow of information through pyramidal cells and regulate the efficacy of the network. We also explore the effect of cellular modification due to neuronal activity and the effect of incorporating spatially dependent connectivity on the network during recall of previously stored information. In particular we implement a spiking neural network proposed by Sommer and Wennekers (2001). We consider methods for improving associative memory recall using methods inspired by the work by Graham and Willshaw (1995) where they apply mathematical transforms to an artificial neural network to improve the recall quality within the network. The networks tested contain either 100 or 1000 pyramidal cells with 10% connectivity applied and a partial cue instantiated, and with a global pseudo-inhibition.We investigate three methods. Firstly, applying localised disynaptic inhibition which will proportionalise the excitatory post synaptic potentials and provide a fast acting reversal potential which should help to reduce the variability in signal propagation between cells and provide further inhibition to help synchronise the network activity. Secondly, implementing a persistent sodium channel to the cell body which will act to non-linearise the activation threshold where after a given membrane potential the amplitude of the excitatory postsynaptic potential (EPSP) is boosted to push cells which receive slightly more excitation (most likely high units) over the firing threshold. Finally, implementing spatial characteristics of the dendritic tree will allow a greater probability of a modified synapse existing after 10% random connectivity has been applied throughout the network. We apply spatial characteristics by scaling the conductance weights of excitatory synapses which simulate the loss in potential in synapses found in the outer dendritic regions due to increased resistance. To further increase the biological plausibility of the network we remove the pseudo-inhibition and apply realistic basket cell models with differing configurations for a global inhibitory circuit. The networks are configured with; 1 single basket cell providing feedback inhibition, 10% basket cells providing feedback inhibition where 10 pyramidal cells connect to each basket cell and finally, 100% basket cells providing feedback inhibition. These networks are compared and contrasted for efficacy on recall quality and the effect on the network behaviour. We have found promising results from applying biologically plausible recall strategies and network configurations which suggests the role of inhibition and cellular dynamics are pivotal in learning and memory