Introduction to Computational Neuroscience

ESAM 495

Hermann Riecke

TuTh 9:30-11:00 M177 Technological Institute

This class is intended for an interdisciplinary audience of applied mathematicians, biologists, engineers, physicists.

For detailed class information see bottom of the page

Outline

1. Introduction
2. Single Neurons:
   1. Passive properties
   2. Ion Channels, Nernst-Planck equation and equilibrium, Goldman-Hodgkin-Katz equation
   3. Hodgkin-Huxley model
   4. Conductance-Based Models: Additional currents $I_{A}$, $I_{CaT}$, $I_{KCa}$
   5. Integrate-and-Fire model (Type-I vs Type-II neurons)
3. Cable equation
   1. Linear Cable Theory
   2. Axons and Active Dendrites
      Movie
4. Synapses
   1. gap junctions
   2. chemical synapses, facilitation and depression
5. Firing-Rates
   1. Poisson spike trains
   2. Spike-triggered average, receptive fields
6. Networks:
   1. Rate Models
   2. Feed-forward Networks
      1. V1: Hubel-Wiesel model Long Movie Short Movie
      2. Compensation of gaze direction
   3. Recurrent Networks
      1. Limulus vision: center-surround cells, temporal on/off cells, selective amplification
      2. Associate memory: Hopfield network
7. Networks: Spiking Neurons
   1. Synchronization: weak coupling and phase-response curve
   2. Gamma-rhythm
8. Unsupervised Learning
   1. Hebbian rule, Oja rule, BCM rule
   2. Development of ocular dominance
9. Synaptic Plasticity, Spike-Timing-Dependent Plasticity
10. Neural Decoding
    discrimination, population decoding, optimal decoding, Fisher information
11. Information theory
    entropy maximization, decorrelation, whitening filter

The class will be based largely on the book Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press). For Northwestern students it is available online at Theoretical Neuroscience. The book is, however, really worth bying.

Lecture notes are also available online for Northwestern students or for general audience. They will be updated as the class proceeds. Therefore it is highly recommended only to download the currently used section, even if more sections should already be available. Please note that the notes are only available from computers on the northwestern.edu subnet.

Other recommended sources:

1. The class has substantial overlap with the class W.L. Kath taught in Winter 2007. His notes are at Kath's Notes.
2. J. Keener and J. Sneyd, Mathematical Physiology
   It is available online at Mathematical Physiology. This is also a good book. The overlap with the class is, however, smaller and from that perspective the online version will be fine. We'll mostly use it for the derivation of the Goldmann-Hodgkin-Katz equation.
3. P. Churchland, T.J. Sejnowski, The Computational Brain
   It is available online at The Computational Brain. It has a good overview of brain function and basic anatomy.
4. Brain Facts published by the Society for Neuroscience, available online at Brain Facts
5. hhsim simulator by D. Touretzky et al. for Hodgkin-Huxley model with exercises (see also HHsim home page)

There won't be class on October 16 and November 18. The time will be made up. Office Hours
Mo 3-4, Tu 11-12, Thu 11-12 in M458 Homework Assignments:
HW 1
Matlab programs for this assignment: Problem 2 Problem 3 sketch of solutions
HW 2 You will need to obtain a few journal articles, as discussed in the assignment. Partial Solutions
HW 3 Partial Solutions Sample Matlab program
HW 4 Partial Solutions HW 5 pattern 1 pattern 2 pattern 3 pattern 4

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