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Volga Neuroscience School 2016 Astroglial control of rhythm genesis in the brain
Two-Theta Neuron Model: Novel Phase Reduced Model Explored in Central Pattern Generators
Aaron Kelley* and Andrey Shilnikov
Georgia State University, 100 Piedmont Ave SE, Atlanta, USA. * Presenting e-mail: akelley11@student.gsu.edu
We explore dynamical foundations of rhythmogenesis and its stability in neural circuits using a reduced, 2-theta phase model for bursting cells. Of special interest are central pattern generators (CPG) capable of producing multiple [co-existing] bursting patterns/outcomes with specific and robust phase lags that underlie and determine a variety of locomotion functions of animals. Biological applications include models and emulation of swim CPGs of sea slugs such as Tritonia, Melibe, and Dendronotus, as well as lobster pyloric networks.
We show how key features of network dynamics, including robustness, occurrence, and metamorphoses of rhythmic outcomes, can be disclosed and evaluated using 2D return maps for phase-lags that provide the comprehensive network characterization in terms of fixed points, invariant circles and their stability and bifurcations. We show a de-facto proof of the excellent agreement between dynamics of networks comprised of phenomenologically reduced phase models and biologically plausible Hodgkin-Huxley type bursters with chemical and electrical synapses.
The versatility of our approach allows us to extend the model's applicability to larger neural networks, specifically ones with modular organization. The 2-theta neuron model also offers the benefit of greatly reducing computation costs and simplifies constructing large networks with complex intrinsic connectivity.
Development of a Method for the Estimation of Gap-Junctional Parameters
I. Falk1* and Y. Timofeeva2
1 Mathematics institute, University of Warwick, Coventry, CV4 7AL, United Kingdom;
2 Department of Computer Science and Centre for Complexity Science, University of Warwick , Coventry, CV4 7AL,
United Kingdom. * Presenting e-mail: isak.falk@live.se
Gap junctions, also referred to as electrical synapses in neuronal cells, are expressed along the entire central nervous system and are important in mediating various brain rhythms in both normal and pathological states. They are mechanical and electrically conductive links between two adjacent cells that allow the passage of ions and small molecules from the cytosol of one cell to the cytosol of its neighbouring cell. Many instances of gap-junctional coupling are formed between dendritic arbours of individual neuronal cells. Locations and strengths of these distal gap junctions in real neuronal networks are often difficult to measure experimentally. Here we aim to develop an approach for predicting these gap-junctional parameters from a limited number of somatic stimulations. Our approach employs a recently developed method for analytically constructing a response function on gap junction-coupled neuronal networks [1]. It can be applied to simplified neuronal morphologies obtained by a reduction method shown in [1] as well as to more biologically realistic complex structures. Although the focus here is on a neuronal network, the method can be easily modified for a network of astrocytes interconnected through gap junction channels and communicating by intercellular calcium signalling [2, 3].
References
1. L. Yihe and Y. Timofeeva, Biol. Cybern., 2016, pp 1-17, DOI: 10.1007/s00422-016-0681-y.
2. C. Giaume, A. Koulakoff, L. Roux, D. Holcman, and N. Rouach, Nat. Rev. Neurosci., 11, 87-99, 2010.
3. A. Volterra, N. Liaudet, and I. Savtchouk, Nat. Rev. Neurosci., 15, 327-335, 2014.
OM&P
Opera Med Physiol 2016 Vol. 2 (S1) 99
