2010 — 2014 |
Shilnikov, Andrey |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Multistability and Bifurcations For Polyrhythmic Central Pattern Generators @ Georgia State University Research Foundation, Inc.
The project will develop the dynamical principles of multistability of bursting patterns of polyrhythmic activity and its control for multifunctional Central Pattern Generators. Multistability enhances the flexibility of nervous systems and has far reaching implications for motor control, dynamic memory, information processing, and decision making. The Investigator and his students will identify and study generic nonlocal bifurcations of bursting rhythms in realistic models of single and networked interneurons, as well as create a dynamical systems classification for the bursting genesis in CPGs. The research team will create a suite of new methods and computational tools based on the theory of dynamical systems and global bifurcations to examine complex transformations of bursting patterns in high-order Hodgkin-Huxley type models and networks. The Investigator and his students will enhance the existing mathematical technique by creating transparent computational tools for the detection and prediction of transformations of complex oscillatory solutions in neuronal models with multiple time scales. This includes the novel approaches of reducing neuronal dynamics to a complete, equation-free family of onto Poincaré mappings for membrane potentials, and the phase-difference mappings for bursting CPG circuits. The reduction will yield a clear understanding of the dynamics of a high-order, multiple-time scale neuron model, as well as provide with a control of the multistability by revealing the hidden centers that govern globally the dynamics of a mutlifunctional CPG network. Having the extensive knowledge of dynamical properties of networked busting interneurons will allow the team to derive precise phase models to replicate the dynamics of their high-dimensional models. These reduced models will be used to examine larger and more complex realistic models of the specific excitatory-inhibitory CPG circuits.
The ability of distinct anatomical circuits, like Central Pattern Generators, to generate multiple patterns of neural activity to control several locomotion types, like cardiac beating, waking, swimming etc, is widespread among vertebrate and invertebrate species. Understanding generic mechanisms of the evolution of neuronal connectivity and transitions between different patterns of neural activity and modeling these processes are the fundamental challenges for applied mathematics and computational neuroscience. This project is a genuinely cross-disciplinary research, bridging state-of the art mathematics, more specifically the theory of applied dynamical systems and nonlocal bifurcations, with life sciences. It shall extend and generalize our understanding of dynamical principles of neural systems; specifically mechanisms regulating polyrhythms of multifunctional Central Pattern Generators. Multistability enhances the flexibility of nervous systems and has far reaching implications for motor control, dynamic memory, information processing, and decision making of humans and animals. The Investigator and his students will identify and study generic bifurcations of bursting rhythms in realistic models of single and networked interneurons, as well as create a dynamical systems classification for the bursting genesis in multifunctional neural circuits.
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2015 — 2019 |
Katz, Paul [⬀] Shilnikov, Andrey |
N/AActivity Code Description: No activity code was retrieved: click on the grant title for more information |
Neural Mechanisms Underlying Evolvability of Behavior @ Georgia State University Research Foundation, Inc.
This project examines fundamental questions about the features of neural circuits that affect the evolution of behavior. The species being examined are nudibranch sea slugs, which have highly accessible nervous systems that allow experiments to be conducted that are not feasible in other types of animals. The brains of nudibranchs contain only about 10,000 nerve cells (neurons), many of which can be individually identified from animal to animal within a species. Furthermore, neurons can often be identified across different species. Electrical activity can be recorded from multiple neurons to reveal neural circuitry. The connectivity of those circuits can be compared across species. This research team found that although the species have the same sets of neurons, they are wired up differently, even when the species produce similar behaviors. One goal of the project is to artificially rewire the neurons in one species to produce the neural circuit of another species and to create mathematical models that do the same. This will establish how easy it is to convert the behavior of one species into that of another. It also contributes to understanding the basic rules for generating behavior by comparing across species instead of focusing on a single species. The project engages the public by soliciting observations of nudibranch behavior from divers around the world through social media. It also provides important research opportunities to under-represented students through a research pipeline and creates resources that will be available to the scientific community to aid in identifying neurons and mapping out circuits.
Evolvability reflects the ability to evolve. This project examines the features of neural circuits that affect the evolvability of swimming behaviors in nudibranchs. The project uses a variety of techniques to achieve its goals. First, transcriptomics is used to resolve the phylogeny of the Nudibranchia and allow phylogenic hypotheses to be tested. The brain transcriptomes further aid in the discovery of molecular markers for identified neurons, which are needed particularly in species that do not swim. Electrophysiological techniques are used to search for "latent" circuitry, that is, connectivity that might be present in non-swimmers and potentially activated by small changes. These changes will be applied using the dynamic clamp technique to inject artificial synaptic and membrane conductances and through ectopic expression of serotonin receptors. Finally, mathematical simulations are used to examine the consequences of different circuit architectures and their robustness for rhythmic activity.
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