Elucidating the Interplay of Structure, Dynamics, and Function in the Brain’s Neural Networks.

Brain’s structure, dynamics, and function are deeply intertwined. To understand how the brain functions, it is crucial to uncover the links between network structure and its dynamics. Here I examine different approaches to exploring the key connecting factors between network structure, dynamics and eventually its function. I predominantly concentrate on emergence and temporal evolution of synchronization, or coincidence of neuronal spike timings, as it has been associated with many brain functions while aberrant synchrony is implicated in many neurological disorders. Specifically, in chapter II, I investigate how the interplay of cellular properties with network coupling characteristics could affect the propensity of neural networks for synchronization. Then, in chapter III, I develop a set of measures that identify hallmarks and potentially predict autonomous network transitions from asynchronous to synchronous dynamics under various conditions. The developed metrics can be calculated in real time and therefore potentially applied in clinical situations. Finally, in chapter IV, I aim to tie the correlates of neural network dynamics to the brain function. More specifically, I elucidate dynamical underpinnings of learning and memory consolidation from in vivo recordings of mice experiencing contextual fear conditioning (CFC) and show, that the introduced notion of network stability may predict future animal performance on memory retrieval. Overall, the results presented within this dissertation underscore the importance of concurrent analysis of networks’ dynamical and structural properties. The developed approaches may prove useful beyond the specific application presented within this thesis.PhDBiophysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120768/1/mofakham_1.pd

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires a know-how of all the methodological steps of the processing pipeline that manipulates the input brain signals and extract the functional network properties. On the other hand, a knowledge of the neural phenomenon under study is required to perform physiological-relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes

Beta-rhythm oscillations and synchronization transition in network models of Izhikevich neurons: effect of topology and synaptic type

Despite their significant functional roles, beta-band oscillations are least understood. Synchronization in neuronal networks have attracted much attention in recent years with the main focus on transition type. Whether one obtains explosive transition or a continuous transition is an important feature of the neuronal network which can depend on network structure as well as synaptic types. In this study we consider the effect of synaptic interaction (electrical and chemical) as well as structural connectivity on synchronization transition in network models of Izhikevich neurons which spike regularly with beta rhythms. We find a wide range of behavior including continuous transition, explosive transition, as well as lack of global order. The stronger electrical synapses are more conducive to synchronization and can even lead to explosive synchronization. The key network element which determines the order of transition is found to be the clustering coefficient and not the small world effect, or the existence of hubs in a network. These results are in contrast to previous results which use phase oscillator models such as the Kuramoto model. Furthermore, we show that the patterns of synchronization changes when one goes to the gamma band. We attribute such a change to the change in the refractory period of Izhikevich neurons which changes significantly with frequency.Comment: 7 figures, 1 tabl

Emergence of Spatio-Temporal Pattern Formation and Information Processing in the Brain.

The spatio-temporal patterns of neuronal activity are thought to underlie cognitive functions, such as our thoughts, perceptions, and emotions. Neurons and glial cells, specifically astrocytes, are interconnected in complex networks, where large-scale dynamical patterns emerge from local chemical and electrical signaling between individual network components. How these emergent patterns form and encode for information is the focus of this dissertation. I investigate how various mechanisms that can coordinate collections of neurons in their patterns of activity can potentially cause the interactions across spatial and temporal scales, which are necessary for emergent macroscopic phenomena to arise. My work explores the coordination of network dynamics through pattern formation and synchrony in both experiments and simulations. I concentrate on two potential mechanisms: astrocyte signaling and neuronal resonance properties. Due to their ability to modulate neurons, we investigate the role of astrocytic networks as a potential source for coordinating neuronal assemblies. In cultured networks, I image patterns of calcium signaling between astrocytes, and reproduce observed properties of the network calcium patterning and perturbations with a simple model that incorporates the mechanisms of astrocyte communication. Understanding the modes of communication in astrocyte networks and how they form spatial temporal patterns of their calcium dynamics is important to understanding their interaction with neuronal networks. We investigate this interaction between networks and how glial cells modulate neuronal dynamics through microelectrode array measurements of neuronal network dynamics. We quantify the spontaneous electrical activity patterns of neurons and show the effect of glia on the neuronal dynamics and synchrony. Through a computational approach I investigate an entirely different theoretical mechanism for coordinating ensembles of neurons. I show in a computational model how biophysical resonance shifts in individual neurons can interact with the network topology to influence pattern formation and separation. I show that sub-threshold neuronal depolarization, potentially from astrocytic modulation among other sources, can shift neurons into and out of resonance with specific bands of existing extracellular oscillations. This can act as a dynamic readout mechanism during information storage and retrieval. Exploring these mechanisms that facilitate emergence are necessary for understanding information processing in the brain.PHDApplied PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111493/1/lshtrah_1.pd

Network and cellular mechanisms underlying heterogeneous excitatory/inhibitory balanced states

Recent work has explored spatiotemporal relationships between excitatory (E) and inhibitory (I) signaling within neural networks, and the effect of these relationships on network activity patterns. Data from these studies have indicated that excitation and inhibition are maintained at a similar level across long time periods and that excitatory and inhibitory currents may be tightly synchronized. Disruption of this balance—leading to an aberrant E/I ratio—is implicated in various brain pathologies. However, a thorough characterization of the relationship between E and I currents in experimental settings is largely impossible, due to their tight regulation at multiple cellular and network levels. Here, we use biophysical neural network models to investigate the emergence and properties of balanced states by heterogeneous mechanisms. Our results show that a network can homeostatically regulate the E/I ratio through interactions among multiple cellular and network factors, including average firing rates, synaptic weights and average neural depolarization levels in excitatory/inhibitory populations. Complex and competing interactions between firing rates and depolarization levels allow these factors to alternately dominate network dynamics in different synaptic weight regimes. This leads to the emergence of distinct mechanisms responsible for determining a balanced state and its dynamical correlate. Our analysis provides a comprehensive picture of how E/I ratio changes when manipulating specific network properties, and identifies the mechanisms regulating E/I balance. These results provide a framework to explain the diverse, and in some cases, contradictory experimental observations on the E/I state in different brain states and conditions.Network can homeostatically regulate the E/I ratio and net post‐synaptic current through interactions among multiple cellular and network factors, including average firing rates, synaptic weights and average neural depolarization levels in excitatory/inhibitory neuronal populations, leading to the emergence of distinct mechanisms responsible for determining a balanced E/I state and its dynamical correlate. This in turn leads to the emergence of multiple balance states having different dynamical properties.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154922/1/ejn14669_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154922/2/ejn14669-sup-0001-Supinfo.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154922/3/ejn14669.pd

Efficient Transmission of Subthreshold Signals in Complex Networks of Spiking Neurons

We investigate the efficient transmission and processing of weak, subthreshold signals in a realistic neural medium in the presence of different levels of the underlying noise. Assuming Hebbian weights for maximal synaptic conductances—that naturally balances the network with excitatory and inhibitory synapses—and considering short-term synaptic plasticity affecting such conductances, we found different dynamic phases in the system. This includes a memory phase where population of neurons remain synchronized, an oscillatory phase where transitions between different synchronized populations of neurons appears and an asynchronous or noisy phase. When a weak stimulus input is applied to each neuron, increasing the level of noise in the medium we found an efficient transmission of such stimuli around the transition and critical points separating different phases for well-defined different levels of stochasticity in the system. We proved that this intriguing phenomenon is quite robust, as it occurs in different situations including several types of synaptic plasticity, different type and number of stored patterns and diverse network topologies, namely, diluted networks and complex topologies such as scale-free and small-world networks. We conclude that the robustness of the phenomenon in different realistic scenarios, including spiking neurons, short-term synaptic plasticity and complex networks topologies, make very likely that it could also occur in actual neural systems as recent psycho-physical experiments suggest.The authors acknowledge support from the Spanish Ministry of economy and competitiveness under the project FIS2013-43201-P

Synchronization of coupled neural oscillators with heterogeneous delays

We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of synchronized oscillations of variable period. We analyze this synchronization based on the interplay of the different time delays and support the numerical results by analytical findings. In addition, we elaborate on bursting-like dynamics with two competing timescales on the basis of the autocorrelation function.Comment: 18 pages, 14 figure

Information processing in neural systems: oscillations, network topologies and optimal representations

Tesis doctoral inédita leída en la Universidad Autónoma de Madrid. Escuela Politécnica Superior, Departamento de Ingeniería informática. Fecha de lectura: 1-07-200

Graph theoretical analysis of complex networks in the brain

Since the discovery of small-world and scale-free networks the study of complex systems from a network perspective has taken an enormous flight. In recent years many important properties of complex networks have been delineated. In particular, significant progress has been made in understanding the relationship between the structural properties of networks and the nature of dynamics taking place on these networks. For instance, the 'synchronizability' of complex networks of coupled oscillators can be determined by graph spectral analysis. These developments in the theory of complex networks have inspired new applications in the field of neuroscience. Graph analysis has been used in the study of models of neural networks, anatomical connectivity, and functional connectivity based upon fMRI, EEG and MEG. These studies suggest that the human brain can be modelled as a complex network, and may have a small-world structure both at the level of anatomical as well as functional connectivity. This small-world structure is hypothesized to reflect an optimal situation associated with rapid synchronization and information transfer, minimal wiring costs, as well as a balance between local processing and global integration. The topological structure of functional networks is probably restrained by genetic and anatomical factors, but can be modified during tasks. There is also increasing evidence that various types of brain disease such as Alzheimer's disease, schizophrenia, brain tumours and epilepsy may be associated with deviations of the functional network topology from the optimal small-world pattern