A biophysical model of striatal microcircuits suggests gamma and beta oscillations interleaved at delta/theta frequencies mediate periodicity in motor control

Striatal oscillatory activity is associated with movement, reward, and decision-making, and observed in several interacting frequency bands. Local field potential recordings in rodent striatum show dopamine- and reward-dependent transitions between two states: a "spontaneous" state involving β (∼15-30 Hz) and low γ (∼40-60 Hz), and a state involving θ (∼4-8 Hz) and high γ (∼60-100 Hz) in response to dopaminergic agonism and reward. The mechanisms underlying these rhythmic dynamics, their interactions, and their functional consequences are not well understood. In this paper, we propose a biophysical model of striatal microcircuits that comprehensively describes the generation and interaction of these rhythms, as well as their modulation by dopamine. Building on previous modeling and experimental work suggesting that striatal projection neurons (SPNs) are capable of generating β oscillations, we show that networks of striatal fast-spiking interneurons (FSIs) are capable of generating δ/θ (ie, 2 to 6 Hz) and γ rhythms. Under simulated low dopaminergic tone our model FSI network produces low γ band oscillations, while under high dopaminergic tone the FSI network produces high γ band activity nested within a δ/θ oscillation. SPN networks produce β rhythms in both conditions, but under high dopaminergic tone, this β oscillation is interrupted by δ/θ-periodic bursts of γ-frequency FSI inhibition. Thus, in the high dopamine state, packets of FSI γ and SPN β alternate at a δ/θ timescale. In addition to a mechanistic explanation for previously observed rhythmic interactions and transitions, our model suggests a hypothesis as to how the relationship between dopamine and rhythmicity impacts motor function. We hypothesize that high dopamine-induced periodic FSI γ-rhythmic inhibition enables switching between β-rhythmic SPN cell assemblies representing the currently active motor program, and thus that dopamine facilitates movement in part by allowing for rapid, periodic shifts in motor program execution.R01 MH114877 - NIMH NIH HHSPublished versio

Weak coupling of neurons enables very high-frequency and ultra-fast oscillations through the interplay of synchronized phase-shifts

Recently, in the past decade, high-frequency oscillations (HFOs), very high-frequency oscillations (VHFOs), and ultra-fast oscillations (UFOs) were reported in epileptic patients with drug-resistant epilepsy. However, to this day, the physiological origin of these events has yet to be understood. Our study establishes a mathematical framework based on bifurcation theory for investigating the occurrence of VHFOs and UFOs in depth EEG signals of patients with focal epilepsy, focusing on the potential role of reduced connection strength between neurons in an epileptic focus. We demonstrate that synchronization of a weakly coupled network can generate very and ultra high-frequency signals detectable by nearby microelectrodes. In particular, we show that a bistability region enables the persistence of phase-shift synchronized clusters of neurons. This phenomenon is observed for different hippocampal neuron models, including Morris-Lecar, Destexhe-Paré, and an interneuron model. The mechanism seems to be robust for small coupling, and it also persists with random noise affecting the external current. Our findings suggest that weakened neuronal connections could contribute to the production of oscillations with frequencies above 1000Hz, which could advance our understanding of epilepsy pathology and potentially improve treatment strategies. However, further exploration of various coupling types and complex network models is needed

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

Simulations of Neocortical Columnar Oscillations

The intentionof this thesis is to examine the role of the neocortical local drcuit in supporting synchronisatLon and fast (gamma) oscUlation. The aim is to include stereotypical features of the local neocortex in model simulations of cortical activity. Modelling is hmitedby scale in number and detail. Model features include three neurontypes(RS, FS and IB) andsynapses with three time courses takenfrom reportedtri-phasic PSPs (fEPSP, flPSP andsIPSP). Cell types and synapses are distributedin a two layer model. The contribution of the layers to columnactivity is investigated. The upperlayer has a tendancy towardspredse synchronisation and can dominate the activity producing synchronisation and oscillation in the whole column. This is attributed to the stronger inhibitory circuit in the upperlayer. The lower layer achieves a less precise synchronisatiorv this is attributed to a lower level of inhibition and the intraburst duration of IB neurons. The significance of this difference in the temporal properties of the two layers is discussed in relation to existing theories andmodels of local cortical function. Following a further consideration of local cortical physiology a new model of cortical functioning is proposed. The key features of this model include: the generation of local oscillations in a vertical interlarninar reciprocal circuit; the apical dendrite providing a sharp coincidence detection functionbetweenthe layers; slow axonal lateral propagationprovidinga time delay network; apical dendrites of bursting cells (CH and IB) providing coincidence detectionbetweenmputs 6:0m distant areas (layer 1 inputs) and local activity; bursting cell innervationof intemeurons, linking the local oscillation cy de to coinddence detection. This moddis termed an'intrinsically osdllating time coding networld (lOTCN). Specific predictions are made concerning the functiorungof the local circuit m neocortex, and the connectivity of CH neurons

Synchronization Behavior in Coupled Chemical Oscillators

Synchronization is a collective phenomenon emerging from the interactions of different dynamical systems. Systems with different characteristics adjust their behavior to a common behavior of the group. This collective behavior is observed in many biological, chemical, and physical systems. Examples from different fields include pacemaker heart cells, synchronization of neurons during epilepsy seizures, arrays of microwave oscillators, and robot manipulators. Studies of coupled oscillators have revealed different mechanisms by which discrete oscillators interact and organize to a uniform synchronized state from an incoherent state. The discovery of a new type of synchronization state, called the chimera state has further broadened the field of synchronization. A chimera state is made up of coexisting subpopulations of oscillators, each with same coupling structure, but with one exhibiting synchronous behavior and the other asynchronous behavior. The phenomena has been the focus of much theoretical and experimental research in the past decade. In this thesis, experimental and simulation studies of chimera states in populations of coupled chemical oscillators will be described and their relation to other synchronization states will be characterized. Experiments were carried out with the photosensitive Belousov-Zhabotinsky (BZ) chemical oscillators and a light feedback scheme. The dimensionless two-variable Zhabotinsky-Buchholtz-Kiyatin-Epstein (ZBKE) model of the BZ chemical system was used in simulations.;A two-group coupling model, which splits the oscillators into two subpopulations, was used in the first part of the study. The subpopulations are globally coupled, both within and between the subpopulations. The coupling of every oscillator with members of the other subpopulation is weaker than the coupling with members of its own subpopulation. In-phase, out-of-phase, and phase-cluster synchronized states, as well as the chimera state, were found in both experiments and simulations. The probability of finding a chimera state decreases with increasing intra-group coupling strength. The study also revealed that heterogeneity in the frequencies of the oscillators in the system decreases the lifetime of a chimera. This was evidenced by the collapse of the chimera state to a synchronized state in both experiments and simulations with heterogeneous oscillators.;Synchronized and mixed-state behaviors are observed in populations of nonlocally coupled chemical oscillators in a ring configuration. With nonlocal coupling, the nearest neighbors are strongly coupled and the coupling strength decreases exponentially with distance. Experimental studies show stable chimera states, phase cluster states and phase waves coexisting with unsychronized groups of oscillators. These are spontaneously formed from quasi-random initial phase distributions in the experiments and random initial phase distributions in simulations. Simulations with homogeneous and heterogeneous oscillators revealed that a finite spread of frequencies increases the probability of initiating a synchronized group, leading to chimera states. The effects of group size and coupling strength on chimera states, phase waves, phase clusters, and traveling waves are discussed. Complex behaviors in coexisting states were analyzed, consisting of periodic phase slips with identical oscillators and periodic switching with nonidentical oscillators. Fourier transform analysis was used to distinguish between states exhibiting high periodicity and chimera states, which show similar average behavior

Neuronal Synchronization Can Control the Energy Efficiency of Inter-Spike Interval Coding

The role of synchronous firing in sensory coding and cognition remains controversial. While studies, focusing on its mechanistic consequences in attentional tasks, suggest that synchronization dynamically boosts sensory processing, others failed to find significant synchronization levels in such tasks. We attempt to understand both lines of evidence within a coherent theoretical framework. We conceptualize synchronization as an independent control parameter to study how the postsynaptic neuron transmits the average firing activity of a presynaptic population, in the presence of synchronization. We apply the Berger-Levy theory of energy efficient information transmission to interpret simulations of a Hodgkin-Huxley-type postsynaptic neuron model, where we varied the firing rate and synchronization level in the presynaptic population independently. We find that for a fixed presynaptic firing rate the simulated postsynaptic interspike interval distribution depends on the synchronization level and is well-described by a generalized extreme value distribution. For synchronization levels of 15% to 50%, we find that the optimal distribution of presynaptic firing rate, maximizing the mutual information per unit cost, is maximized at ~30% synchronization level. These results suggest that the statistics and energy efficiency of neuronal communication channels, through which the input rate is communicated, can be dynamically adapted by the synchronization level.Comment: 47 pages, 14 figures, 2 Table

Convergence of Action, Reaction, and Perception via Neural Oscillations in Dynamic Interaction with External Surroundings

There has been a considerable interest in the role of time-dimension in functions of the brain, which has been limited to time perception and timing of behavior. However, during past few years it has become increasingly clear that the role of the time-dimension includes other complex cognitive functions, such as motor control of a vehicle, sensory perception and processing imageries to name a few. Role of the accurate representation of time-dimension is important for several neural mechanisms, which include temporal coupling, coincidence detection, and processing of Shannon information. These mechanisms play key roles in processing information during the interaction of the brain with the physical surroundings

Study of perturbations of an oscillating neuronal network via phase-amplitude response functions

Phase reduction is a powerful tool for understanding the behavior of perturbed oscillators. It allows for the description of high-dimensional oscillatory systems in terms of a single variable, the phase. Alternatively, mean-field models are a viable option to make the analysis of large systems more tractable. In this work, we apply a phase-amplitude technique on a mean-field model for a network of quadratic integrate-and-fire neurons, which is exact in the thermodynamic limit. This methodology allows us to compute the global isochrons and isostables of the system, and a generalization of the phase response curve beyond the limit cycle constraint: the phase and amplitude response functions. We compare the perturbed dynamics of the oscillating mean-field system with its N-dimensional counterpart, which also exhibits synchronized spiking, and observe how the response functions are able to predict accurately the evolution of the network. Moreover, since the model exhibits slow-fast dynamics, the method yields a dimensionality reduction restricted to the slow stable manifold of the system

Central aspects of systemic oestradiol negative‐ and positive‐feedback on the reproductive neuroendocrine system

The central nervous system regulates fertility via the release of gonadotrophin‐releasing hormone (GnRH). This control revolves around the hypothalamic‐pituitary‐gonadal axis, which operates under traditional homeostatic feedback by sex steroids from the gonads in males and most of the time in females. An exception is the late follicular phase in females, when homeostatic feedback is suspended and a positive‐feedback response to oestradiol initiates the preovulatory surges of GnRH and luteinising hormone. Here, we briefly review the history of how mechanisms underlying central control of ovulation by circulating steroids have been studied, discuss the relative merit of different model systems and integrate some of the more recent findings in this area into an overall picture of how this phenomenon occurs.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/153639/1/jne12724.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/153639/2/jne12724_am.pd