Complex Dynamics in Dedicated / Multifunctional Neural Networks and Chaotic Nonlinear Systems

We study complex behaviors arising in neuroscience and other nonlinear systems by combining dynamical systems analysis with modern computational approaches including GPU parallelization and unsupervised machine learning. To gain insights into the behaviors of brain networks and complex central pattern generators (CPGs), it is important to understand the dynamical principles regulating individual neurons as well as the basic structural and functional building blocks of neural networks. In the first section, we discuss how symbolic methods can help us analyze neural dynamics such as bursting, tonic spiking and chaotic mixed-mode oscillations in various models of individual neurons, the bifurcations that underlie transitions between activity types, as well as emergent network phenomena through synergistic interactions seen in realistic neural circuits, such as network bursting from non-intrinsic bursters. The second section is focused on the origin and coexistence of multistable rhythms in oscillatory neural networks of inhibitory coupled cells. We discuss how network connectivity and intrinsic properties of the cells affect the dynamics, and how even simple circuits can exhibit a variety of mono/multi-stable rhythms including pacemakers, half-center oscillators, multiple traveling-waves, fully synchronous states, as well as various chimeras. Our analyses can help generate verifiable hypotheses for neurophysiological experiments on central pattern generators. In the last section, we demonstrate the inter-disciplinary nature of this research through the applications of these techniques to identify the universal principles governing both simple and complex dynamics, and chaotic structure in diverse nonlinear systems. Using a classical example from nonlinear laser optics, we elaborate on the multiplicity and self-similarity of key organizing structures in 2D parameter space such as homoclinic and heteroclinic bifurcation curves, Bykov T-point spirals, and inclination flips. This is followed by detailed computational reconstructions of the spatial organization and 3D embedding of bifurcation surfaces, parametric saddles, and isolated closed curves (isolas). The generality of our modeling approaches could lead to novel methodologies and nonlinear science applications in biological, medical and engineering systems

Rhythmogenesis and Bifurcation Analysis of 3-Node Neural Network Kernels

Central pattern generators (CPGs) are small neural circuits of coupled cells stably producing a range of multiphasic coordinated rhythmic activities like locomotion, heartbeat, and respiration. Rhythm generation resulting from synergistic interaction of CPG circuitry and intrinsic cellular properties remains deficiently understood and characterized. Pairing of experimental and computational studies has proven key in unlocking practical insights into operational and dynamical principles of CPGs, underlining growing consensus that the same fundamental circuitry may be shared by invertebrates and vertebrates. We explore the robustness of synchronized oscillatory patterns in small local networks, revealing universal principles of rhythmogenesis and multi-functionality in systems capable of facilitating stability in rhythm formation. Understanding principles leading to functional neural network behavior benefits future study of abnormal neurological diseases that result from perturbations of mechanisms governing normal rhythmic states. Qualitative and quantitative stability analysis of a family of reciprocally coupled neural circuits, constituted of generalized Fitzhugh–Nagumo neurons, explores symmetric and asymmetric connectivity within three-cell motifs, often forming constituent kernels within larger networks. Intrinsic mechanisms of synaptic release, escape, and post-inhibitory rebound lead to differing polyrhythmicity, where a single parameter or perturbation may trigger rhythm switching in otherwise robust networks. Bifurcation analysis and phase reduction methods elucidate qualitative changes in rhythm stability, permitting rapid identification and exploration of pivotal parameters describing biologically plausible network connectivity. Additional rhythm outcomes are elucidated, including phase-varying lags and broader cyclical behaviors, helping to characterize system capability and robustness reproducing experimentally observed outcomes. This work further develops a suite of visualization approaches and computational tools, describing robustness of network rhythmogenesis and disclosing principles for neuroscience applicable to other systems beyond motor-control. A framework for modular organization is introduced, using inhibitory and electrical synapses to couple well-characterized 3-node motifs described in this research as building blocks within larger networks to describe underlying cooperative mechanisms

Effects of coupling and heterogeneity in the pre-Botzinger complex cells using first return maps

The preBotzinger complex located at the ventrolateral medulla in the brainstem is believedto have an important role in generating the respiratory rhythm in mammals, specially theinspiratory process [56]. Keeping this in mind, we will study a small network of such cellsby means of a minimal model suggested and experimentally tested by Butera et al [6, 7]. Athorough analysis of the Butera model was done for two very small networks of pre-Botzingercells: a self coupled single cell and a network of two coupled cells [5]. In order to understandthe role of coupling and heterogeneity in these two particular networks we reduce the selfcoupled single cell network to a one dimensional map using a similar approach as in [37].Using this one dimensional map, some analytical conditions for switching from one regime toanother are determined and numerical results are shown. Using the same idea as for the selfcoupled single cell case, two identical coupled cells are reduced to a two dimensional iteratedmap which is a composition of many one dimensional maps. Using the form of these maps,mechanisms for the transition between previously observed regimes [5] are determined andlinear analysis is performed for a particular set of parameters.Introducing heterogeneity on the network of two coupled identical cells, for a fixed levelof synaptic input, shows that depending on the level of the synaptic input some differentbehaviors arise which were not previously observed in a network of homogenous cells [5].These results suggest that introducing heterogeneity can increase the range in the parameterspace for which cells are bursting. This is desirable, since from experiments it is observedthat bursting is associated with the inspiratory rhythm of respiration

Analysis and modelling of the PY complex in the pyloric circuit of the crab stomatogastric ganglion

PhD ThesisCentral pattern generators (CPGs) are neural circuits that control rhythmic motor patterns such as walking running and swallowing. Injuries can sever the spinal cord or conditions such as Huntington's disease and Parkinson's disease can damage nerves from the brain that control CPGs. Understanding the connectivity of neural circuits has proved insu cient to understand the dynamics of such circuits. Neuromodulators and neurohormones can di erentially a ect every connection in neural circuits and di erent circuits are a ected in very di erent ways. The resulting complexity of such systems make them very di cult to study but research is greatly facilitated by the use of model organisms and computational models. The crustacean stomatogastric ganglion (STG) has been used as a model system for many years. Its relative simplicity and accessibility to neurons makes it an ideal system for the study of neural interaction, CPGs and the e ect of neuromodulators on neural systems. The e ect of dopamine on the pyloric CPG of the crab STG was recorded using voltage sensitive dye imaging and electrophysiological techniques. To analyse voltage sensitive dye (VSD) imaging data a heuristic method was devised that uses the timing of the activity plateaus of neurons for the estimation of the dynamics of the temporal relationship of the neurons' activities. MATLABR was used to create a Hodgkin-Huxley based model of the pyloric constrictor pyloric dilator neurons (PDs) with parameters that could capture the dynamics of neuromodulation. The MATLABR model includes two compartments, the soma and the axon, for the anterior burster neuron, the lateral pyloric neurons (LPs), two PDs and ve individual pyloric constrictor neurons (PYs). By di erentially changing the values of the model synapses, the model is able to reproduce the de-synchronisation of the pyloric constrictor neurons as was observed experimentally i on the dea erented stomatogastric nervous system. Existing models model PYs and PDs as single neurons. These models are unable to show the desynchronising e ect of dopamine on multiple neurons of the same type. The model created for this research is able to re ect the e ect of neuromodulation on the complete circuit by allowing parameters of synapses between neurons of the same type to be adjusted di erentially, re ecting the biological system more accurately

Approaches for unveiling the kinetic mechanisms of voltage gated ion channels in neurons

Includes vitaIonic currents drive cellular function within all living cells to perform highly specific tasks. For excitable cells, such as muscle and neurons, voltage-gated ion channels have finely tuned kinetics that allow the transduction of Action potentials to other cells. Voltage-gated ion channels are molecular machines that open and close depending on electrical potential. Neuronal firing rates are largely determined by the overall availability of voltage-gated Na+ and K+ currents.This work describes new approaches for collecting and analyzing experimental data that can be used to streamline experiments. Ion channels are composed of multimeric complexes regulated by intracellular factors producing complex kinetics. The stochastic behavior of thousands of individual ion hannels coordinates to produce cellular activity. To describe their activity and test hypotheses about the channel, experimenters often fit Markov models to a set of experimental data. Markov models are defined by a set of states, whose transitions described by rate constants. To improve the modeling process, we have developed computational approaches to introduce kinetic constraints that reduces the parameter search space. This work describes the implementation and mathematical transformations required to describe linear and non-linear parameter constraints that govern rate constants. Not all ion channel behaviors can easily be described by rate constants. Therefore, we developed and implemented a penalty-based mechanism that can be used to guide the optimization engine to produce a model with a desired behavior, such as single-channel open probability and use dependent effects. To streamline data collection for experiments in brain slice preparations, we developed a 3D virtual software environment that incorporates data from micro-positioning motors and scientific cameras in real-time. This environment provides positional feedback to the investigator and allows for the creation of data maps including both images and electrical recordings. We have also produced semi-automatic targeting procedures that simplifies the overall experimental experience. Experimentally, this work also examines how the kinetic mechanism of voltage gated Na channels regulates the neuronal firing of brainstem respiratory neurons. These raphe neurons are intrinsic pacemakers that do not rely on synaptic connections to elicit activity. I explored how intracellular calcium regulates the kinetics of TTX-sensitive Na+ currents using whole-cell patch clamp electrophysiology. Established with intracellular Ca2+ buffers, high [Ca2+] levels greater than ~7 [micro]M did not change the voltage dependence of steady-state activation and inactivation, but slightly slowed inactivation time course. However, the recovery from inactivation and use dependence inactivation is slowed by high intracellular [Ca2+]. Overall, these approaches described in this work have improved data acquisition and data analysis to create better ion channel models and enhance the electrophysiology experience.Includes bibliographical reference

25th Annual Computational Neuroscience Meeting: CNS-2016

Abstracts of the 25th Annual Computational Neuroscience Meeting: CNS-2016 Seogwipo City, Jeju-do, South Korea. 2–7 July 201