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

Synchronization of electrically coupled resonate-and-fire neurons

Electrical coupling between neurons is broadly present across brain areas and is typically assumed to synchronize network activity. However, intrinsic properties of the coupled cells can complicate this simple picture. Many cell types with strong electrical coupling have been shown to exhibit resonant properties, and the subthreshold fluctuations arising from resonance are transmitted through electrical synapses in addition to action potentials. Using the theory of weakly coupled oscillators, we explore the effect of both subthreshold and spike-mediated coupling on synchrony in small networks of electrically coupled resonate-and-fire neurons, a hybrid neuron model with linear subthreshold dynamics and discrete post-spike reset. We calculate the phase response curve using an extension of the adjoint method that accounts for the discontinuity in the dynamics. We find that both spikes and resonant subthreshold fluctuations can jointly promote synchronization. The subthreshold contribution is strongest when the voltage exhibits a significant post-spike elevation in voltage, or plateau. Additionally, we show that the geometry of trajectories approaching the spiking threshold causes a "reset-induced shear" effect that can oppose synchrony in the presence of network asymmetry, despite having no effect on the phase-locking of symmetrically coupled pairs

Desynchronization of large-scale neural networks by stabilizing unknown unstable incoherent equilibrium states

In large-scale neural networks, coherent limit cycle oscillations usually coexist with unstable incoherent equilibrium states, which are not observed experimentally. We implement a first-order dynamic controller to stabilize unknown equilibrium states and suppress coherent oscillations. The stabilization of incoherent equilibria associated with unstable focus and saddle is considered. The algorithm is demonstrated for networks composed of quadratic integrate-and-fire (QIF) neurons and Hindmarsh-Rose neurons. The microscopic equations of an infinitely large QIF neural network can be reduced to an exact low-dimensional system of mean-field equations, which makes it possible to study the control problem analytically.Comment: 11 pages, 9 figure

Dynamics and spike trains statistics in conductance-based Integrate-and-Fire neural networks with chemical and electric synapses

We investigate the effect of electric synapses (gap junctions) on collective neuronal dynamics and spike statistics in a conductance-based Integrate-and-Fire neural network, driven by a Brownian noise, where conductances depend upon spike history. We compute explicitly the time evolution operator and show that, given the spike-history of the network and the membrane potentials at a given time, the further dynamical evolution can be written in a closed form. We show that spike train statistics is described by a Gibbs distribution whose potential can be approximated with an explicit formula, when the noise is weak. This potential form encompasses existing models for spike trains statistics analysis such as maximum entropy models or Generalized Linear Models (GLM). We also discuss the different types of correlations: those induced by a shared stimulus and those induced by neurons interactions.Comment: 42 pages, 1 figure, submitte

Local dynamics of gap-junction-coupled interneuron networks

Interneurons coupled by both electrical gap-junctions (GJs) and chemical GABAergic synapses are major components of forebrain networks. However, their contributions to the generation of specific activity patterns, and their overall contributions to network function, remain poorly understood. Here we demonstrate, using computational methods, that the topological properties of interneuron networks can elicit a wide range of activity dynamics, and either prevent or permit local pattern formation. We systematically varied the topology of GJ and inhibitory chemical synapses within simulated networks, by changing connection types from local to random, and changing the total number of connections. As previously observed we found that randomly coupled GJs lead to globally synchronous activity. In contrast, we found that local GJ connectivity may govern the formation of highly spatially heterogeneous activity states. These states are inherently temporally unstable when the input is uniformly random, but can rapidly stabilize when the network detects correlations or asymmetries in the inputs. We show a correspondence between this feature of network activity and experimental observations of transient stabilization of striatal fast-spiking interneurons (FSIs), in electrophysiological recordings from rats performing a simple decision-making task. We suggest that local GJ coupling enables an active search-and-select function of striatal FSIs, which contributes to the overall role of cortical-basal ganglia circuits in decision-making.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85426/1/ph10_1_016015.pd

Gap junction plasticity as a mechanism to regulate network-wide oscillations

Cortical oscillations are thought to be involved in many cognitive functions and processes. Several mechanisms have been proposed to regulate oscillations. One prominent but understudied mechanism is gap junction coupling. Gap junctions are ubiquitous in cortex between GABAergic interneurons. Moreover, recent experiments indicate their strength can be modified in an activity-dependent manner, similar to chemical synapses. We hypothesized that activity-dependent gap junction plasticity acts as a mechanism to regulate oscillations in the cortex. We developed a computational model of gap junction plasticity in a recurrent cortical network based on recent experimental findings. We showed that gap junction plasticity can serve as a homeostatic mechanism for oscillations by maintaining a tight balance between two network states: asynchronous irregular activity and synchronized oscillations. This homeostatic mechanism allows for robust communication between neuronal assemblies through two different mechanisms: transient oscillations and frequency modulation. This implies a direct functional role for gap junction plasticity in information transmission in cortex

Theoretical connections between mathematical neuronal models corresponding to different expressions of noise

Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability are strikingly similar