BGGN260 Neurodynamics

Winter 2009

University of California San Diego

Introduction to the nonlinear dynamics of neurons and simple neural systems through nonlinear dynamics, bifurcation theory, and chaotic motions. The dynamics of single cells is considered at different levels of abstraction, e.g., biophysical and "reduced" models for analysis of regularly spiking and bursting cells, their dynamical properties, and their representation in phase space. The dynamics of synaptic plasticity is studied based on relative timing of neural spikes. Advanced topics such as spatiotemporal dynamics of EEG will be presented in guest lectures. Homework exercises will accompany the lectures, and students will work in groups on a final project. Requirements include in-class presentation and submission of a final report.

Projects will be drawn from a range of topics in computational modeling and analysis of dynamics in biological and engineered neural systems, based on the research interests of the students. Interdisciplinary approaches are highly recommended, such as projects involving VLSI design of dynamical neural systems implemented in silicon circuits.

Instructor: Prof. Gert Cauwenberghs, Pacific Hall 3100E, x46938, gert@ucsd.edu
Office hours: Th 11-noon, or by appointment

TAs: Doug Rubino and Dave Matthews

Time and location: TuTh 9:30-10:50, Pacific Hall 3501

Units: 4

Schedule:

Reference materials:

  • Christof Koch, Biophysics of Computation-- Information Processing in Single Neurons, Oxford University Press, 1999 (with several chapters available on-line).
  • Eugene M. Izhikevich, Dynamical Systems in Neuroscience-- The Geometry of Excitability and Bursting, MIT Press, 2007 (with some chapters and neural data available on-line).
  • Peter Dayan and Larry Abbott, Theoretical Neuroscience-- Computational and Mathematical Modeling of Neural Systems, MIT Press, 2001.
  • Bertil Hille, Ion Channels of Excitable Membranes, 3rd ed., Sinauer Associates, 2001.
  • Wulfram Gerstner and Werner Kistler, Spiking Neural Models: Single Neurons, Populations, Plasticity, Cambridge University Press, 2002.
  • Paul L. Nunez and Ramesh Srinivasan, Electric Fields of the Brain-- The Neurophysics of EEG, 2nd ed., Oxford University Press, 2006.

    • Recommended reading:

  • A.L. Hodgkin and A.F. Huxley, "A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve", J. Physiol., vol. 117, pp. 500-544, 1952.
  • A. Destexhe, Z.F. Mainen and T.J. Sejnowski, "Synthesis of Models for Excitable Membranes, Synaptic Transmission and Neuromodulation Using a Common Kinetic Formalism", J. Comp. Neuroscience, vol. 1, pp. 195-230, 1994.
  • L.F. Abbott and W. Gerstner, "Homeostasis and Learning through Spike-Timing Dependent Plasticity", Methods and Models in Neurophysics, Elsevier Science, 2004.
  • E. Ros, R. Carrillo, E. Ortigosa, B. Barbour, and R. Agis, "Event-Driven Simulation Scheme for Spiking Neural Networks Using Lookup Tables to Characterize Neuronal Dynamics," Neural Computation, vol. 18, pp. 2959-2993, 2006.