Electrical and Computer Engineering 796:
Models of the Neuron
(Winter 2009)

Objective:

To provide a solid conceptual and quantitative background in the modeling of biological neurons and how they function as computational devices. Practical experience will be gained in modeling neurons from a number of perspectives, including equivalent electrical circuits, nonlinear dynamical systems, and random processes, and an introduction to the mathematics required to understand and implement these different engineering methodologies will be given.

Instructor:

Dr. Ian Bruce,
ITB-A213, ext. 26984.
ibruce@mail.ece.mcmaster.ca

Text:

• C. Koch, Biophysics of computation: information processing in single neurons, Oxford University Press, 1998. (ISBN: 0195104919)
  

References:

• P. Dayan and L. F. Abbott, Theoretical neuroscience, MIT Press, 2001. (ISBN: 0262041995)
• D. Johnston and S. M.-S. Wu, Foundations of cellular neurophysiology, MIT Press, 1994. (ISBN: 0262100533)
• C. Koch and I. Segev, Methods in neuronal modeling - 2nd edition, MIT Press, 1998. (ISBN: 0262112310)
• H. Wilson, Spikes decisions and actions: Dynamical foundatoins of neuroscience, Oxford University Press, 1999. (Hdbk: ISBN 0-19-852431-5; Pbk: ISBN 0-19-852430-7)
• W. Gerstner and W. Kistler, Spiking neuron models: single neurons, populations, plasticity, Cambridge University Press , 2002. (Hdbk: ISBN 0-521-81384-0; Pbk: ISBN 0-521-89079-9) Link to online version.
• F. Rieke, D. Warland, R. de Ruyter van Steveninck, and W. Bialek, Spikes: exploring the neural code, MIT Press, 1996. (ISBN: 0262181746)
• D. L. Snyder and M. I. Miller, Random point processes in time and space, Springer-Verlag, 1991. (ISBN: 0387975772)
• S. H. Strogatz, Nonlinear dynamics and chaos: with applications in physics, biology, chemistry, and engineering, Perseus Books, 2001. (ISBN: 0738204536)
• Various articles from the literature

Neural model simulation software:

• HHsim: Graphical Hodgkin-Huxley Simulator
• NEURON: For computer simulations of neurons and neural networks
• The GEneral NEural SImulation System (GENESIS)

Prerequisite:

A basic undergraduate understanding of electrical circuits, linear systems, ordinary and partial differential equations, probability and random processes, and the ability to program in Matlab.

Course Outline: (subject to change)

Introduction to Biological Neurons and Neural Computation (1 Lecture)

• Basic anatomy and physiology of neurons
• Membrane potential
• Spiking & spike propagation
• Synapses, excitation and inhibition
• Basics of neural computation

Simple Deterministic Models of Neural Excitation (2 Lectures)

• Integrate-and-fire models
• Discharge-rate models
• Simple neural networks

Stochastic Models of Neural Activity (2 Lectures)

• Poisson- and renewal-process models
• Random-walk models

Nonlinear Dynamical Models of Neural Excitation (3 Lectures)

• The Hodgkin-Huxley model
• Ionic channels, activation and inactivation states
• Action potential generation
• Phase-plane analysis of neural excitability
• Nonlinear dynamics

Models of Ion Channel Gating (2 Lectures)

• Ion channel gating schemes
• Markov-process models of gating kinetics
• Stochastic differential equation approximations of gating kinetics

Assessment:

Assignments (3 × 20% = 60%); Project (40%).

Term:

II.

Lectures:

There will be one 2.5-hour lecture per week over ten weeks at 10:00am–12:30pm on Mondays in ITB-A311.

PDFs of the lecture slides will be posted here before each lecture.

Slides for:

Lecture #1 (Tuesday, January 13); Lecture #2 (Monday, January 28) - no new slides
Lecture #3 (Monday, January 26); Lecture #4 (Monday, February 2) - no new slides
Lecture #5 (Monday, February 9); Monday, February 16 - no lecture (Reading Week)
Lecture #6 (Monday, February 23); Lecture #7 (Monday, March 2)
Lecture #8 (Monday, March 9); Lecture #9 (Monday, March 16)
Lecture #10 (Monday, March 23)

Assignment #3:

Useful Matlab file: quiver_scaled.m

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The following illustrates only three forms of academic dishonesty:
1. Plagiarism, e.g. the submission of work that is not one’s own or for which other credit has been obtained.
2. Improper collaboration in group work.
3. Copying or using unauthorized aids in tests and examinations."

Last updated Sunday, March 22, 2009