The Interaction of Intrinsic Dynamics and Network Topology in Determining Network Burst Synchrony

The pre-Bötzinger complex (pre-BötC), within the mammalian respiratory brainstem, represents an ideal system for investigating the synchronization properties of complex neuronal circuits via the interaction of cell-type heterogeneity and network connectivity. In isolation, individual respiratory neurons from the pre-BötC may be tonically active, rhythmically bursting, or quiescent. Despite this intrinsic heterogeneity, coupled networks of pre-BötC neurons en bloc engage in synchronized bursting that can drive inspiratory motor neuron activation. The region's connection topology has been recently characterized and features dense clusters of cells with occasional connections between clusters. We investigate how the dynamics of individual neurons (quiescent/bursting/tonic) and the betweenness centrality of neurons’ positions within the network connectivity graph interact to govern network burst synchrony, by simulating heterogeneous networks of computational model pre-BötC neurons. Furthermore, we compare the prevalence and synchrony of bursting across networks constructed with a variety of connection topologies, analyzing the same collection of heterogeneous neurons in small-world, scale-free, random, and regularly structured networks. We find that several measures of network burst synchronization are determined by interactions of network topology with the intrinsic dynamics of neurons at central network positions and by the strengths of synaptic connections between neurons. Surprisingly, despite the functional role of synchronized bursting within the pre-BötC, we find that synchronized network bursting is generally weakest when we use its specific connection topology, which leads to synchrony within clusters but poor coordination across clusters. Overall, our results highlight the relevance of interactions between topology and intrinsic dynamics in shaping the activity of networks and the concerted effects of connectivity patterns and dynamic heterogeneities

Model-free reconstruction of neuronal network connectivity from calcium imaging signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically unfeasible even in dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct approximations to network structural connectivities from network activity monitored through calcium fluorescence imaging. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time-series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the effective network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (e.g., bursting or non-bursting). We thus demonstrate how conditioning with respect to the global mean activity improves the performance of our method. [...] Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good reconstruction of the network clustering coefficient, allowing to discriminate between weakly or strongly clustered topologies, whereas on the other hand an approach based on cross-correlations would invariantly detect artificially high levels of clustering. Finally, we present the applicability of our method to real recordings of in vitro cortical cultures. We demonstrate that these networks are characterized by an elevated level of clustering compared to a random graph (although not extreme) and by a markedly non-local connectivity.Comment: 54 pages, 8 figures (+9 supplementary figures), 1 table; submitted for publicatio

Synchronization in Neuronal Networks with Electrical and Chemical Coupling

Synchronized cortical activities in the central nervous systems of mammals are crucial for sensory perception, coordination, and locomotory function. The neuronal mechanisms that generate synchronous synaptic inputs in the neocortex are far from being fully understood. This thesis contributes toward an understanding of the emergence of synchronization in networks of bursting neurons as a highly nontrivial, combined effect of chemical and electrical connections. The first part of this thesis addresses the onset of synchronization in networks of bursting neurons coupled via both excitatory and inhibitory connections. We show that the addition of pairwise repulsive inhibition to excitatory networks of bursting neurons induces synchrony, in contrast to one’s expectations. Through stability analysis, we reveal the mechanism underlying this purely synergistic phenomenon and demonstrates that it originates from the transition between different types of bursting, caused by excitatory-inhibitory synaptic coupling. We also report a universal scaling law for the synchronization stability condition for large networks in terms of the number of excitatory and inhibitory inputs each neuron receives, regardless of the network size and topology. In the second part of this thesis, we show that similar effects are also observed in other models of bursting neurons, capable of switching from square-wave to plateau bursting. Finally, in the third part, we report a counterintuitive find that combined electrical and inhibitory coupling can synergistically induce robust synchronization in a range of parameters where electrical coupling alone promotes anti-phase spiking and inhibition induces anti-phase bursting. We reveal the underlying mechanism which uses a balance between hidden properties of electrical and inhibitory coupling to act together to synchronize neuronal bursting. We show that this balance is controlled by the duty cycle of the self-coupled system which governs the synchronized bursting rhythm. This work has potential implications for understanding the emergence of abnormal synchrony in epileptic brain networks. It suggests that promoting presumably desynchronizing inhibition in an attempt to prevent seizures can have a counterproductive effect and induce abnormal synchronous firing

Leaders do not look back, or do they?

We study the effect of adding to a directed chain of interconnected systems a directed feedback from the last element in the chain to the first. The problem is closely related to the fundamental question of how a change in network topology may influence the behavior of coupled systems. We begin the analysis by investigating a simple linear system. The matrix that specifies the system dynamics is the transpose of the network Laplacian matrix, which codes the connectivity of the network. Our analysis shows that for any nonzero complex eigenvalue $\lambda$ of this matrix, the following inequality holds: $\frac{|\Im \lambda |}{|\Re \lambda |} \leq \cot\frac{\pi}{n}$. This bound is sharp, as it becomes an equality for an eigenvalue of a simple directed cycle with uniform interaction weights. The latter has the slowest decay of oscillations among all other network configurations with the same number of states. The result is generalized to directed rings and chains of identical nonlinear oscillators. For directed rings, a lower bound $\sigma_c$ for the connection strengths that guarantees asymptotic synchronization is found to follow a similar pattern: $\sigma_c=\frac{1}{1-\cos\left( 2\pi /n\right)}$. Numerical analysis revealed that, depending on the network size $n$, multiple dynamic regimes co-exist in the state space of the system. In addition to the fully synchronous state a rotating wave solution occurs. The effect is observed in networks exceeding a certain critical size. The emergence of a rotating wave highlights the importance of long chains and loops in networks of oscillators: the larger the size of chains and loops, the more sensitive the network dynamics becomes to removal or addition of a single connection

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

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

From network structure to network reorganization: implications for adult neurogenesis

Networks can be dynamical systems that undergo functional and structural reorganization. One example of such a process is adult hippocampal neurogenesis, in which new cells are continuously born and incorporate into the existing network of the dentate gyrus region of the hippocampus. Many of these introduced cells mature and become indistinguishable from established neurons, joining the existing network. Activity in the network environment is known to promote birth, survival and incorporation of new cells. However, after epileptogenic injury, changes to the connectivity structure around the neurogenic niche are known to correlate with aberrant neurogenesis. The possible role of network-level changes in the development of epilepsy is not well understood. In this paper, we use a computational model to investigate how the structural and functional outcomes of network reorganization, driven by addition of new cells during neurogenesis, depend on the original network structure. We find that there is a stable network topology that allows the network to incorporate new neurons in a manner that enhances activity of the persistently active region, but maintains global network properties. In networks having other connectivity structures, new cells can greatly alter the distribution of firing activity and destroy the initial activity patterns. We thus find that new cells are able to provide focused enhancement of network only for small-world networks with sufficient inhibition. Network-level deviations from this topology, such as those caused by epileptogenic injury, can set the network down a path that develops toward pathological dynamics and aberrant structural integration of new cells.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85406/1/ph10_4_046008.pd

Neural synchrony in cortical networks : history, concept and current status

Following the discovery of context-dependent synchronization of oscillatory neuronal responses in the visual system, the role of neural synchrony in cortical networks has been expanded to provide a general mechanism for the coordination of distributed neural activity patterns. In the current paper, we present an update of the status of this hypothesis through summarizing recent results from our laboratory that suggest important new insights regarding the mechanisms, function and relevance of this phenomenon. In the first part, we present recent results derived from animal experiments and mathematical simulations that provide novel explanations and mechanisms for zero and nero-zero phase lag synchronization. In the second part, we shall discuss the role of neural synchrony for expectancy during perceptual organization and its role in conscious experience. This will be followed by evidence that indicates that in addition to supporting conscious cognition, neural synchrony is abnormal in major brain disorders, such as schizophrenia and autism spectrum disorders. We conclude this paper with suggestions for further research as well as with critical issues that need to be addressed in future studies

Neural synchrony in cortical networks : history, concept and current status

Following the discovery of context-dependent synchronization of oscillatory neuronal responses in the visual system, the role of neural synchrony in cortical networks has been expanded to provide a general mechanism for the coordination of distributed neural activity patterns. In the current paper, we present an update of the status of this hypothesis through summarizing recent results from our laboratory that suggest important new insights regarding the mechanisms, function and relevance of this phenomenon. In the first part, we present recent results derived from animal experiments and mathematical simulations that provide novel explanations and mechanisms for zero and nero-zero phase lag synchronization. In the second part, we shall discuss the role of neural synchrony for expectancy during perceptual organization and its role in conscious experience. This will be followed by evidence that indicates that in addition to supporting conscious cognition, neural synchrony is abnormal in major brain disorders, such as schizophrenia and autism spectrum disorders. We conclude this paper with suggestions for further research as well as with critical issues that need to be addressed in future studies