Electrical and Computer Engineering 796:
Models of the Neuron
(Winter 2019)

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.
email alias: ibruce@ieee.org
email: ibruce@mail.ece.mcmaster.ca

Text:

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

References:

• R. Plonsey and R. C. Barr, Bioelectricity: A Quantitative Approach, 3rd Edition, Springer, 2007.
  Electronic copies (PDF files for each chapter) are free to download from the McMaster Library (available only for computers on the McMaster campus or logged in to the LibAccess system).
• 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)

Helpful background knowledge and skills:

A basic undergraduate understanding of electrical circuits, linear systems, ordinary and partial differential equations, probability and random processes, and some ability to program (preferably 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 ~3-hour lecture per week at 10:30am–1:20pm on Wednesdays in PC-335, starting on January 9.

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

Slides for:

Lecture #1 (Wednesday, January 16); Lecture #2 (Wednesday, January 23) — continuing with slides from previous lecture
Lecture #3 (Wednesday, January 30); Wednesday, February 6—class cancelled due to inclement weather closure
Wednesday, February 13—no lecture (instructor away at conference); Lecture #4 (Wednesday, February 20) — continuing with slides from previous lecture
Lecture #5 (Wednesday, February 27); Lecture #6 (Wednesday, March 6) — continuing with slides from previous lecture
Lecture #7 (Wednesday, March 13); Lecture #8 (Wednesday, March 20) — continuing with slides from previous lecture
Lecture #9 (Wednesday, March 27)

Rinzel & Ermentrout book chapter: RinzelErmentrout1998.pdf

Policy Reminders

"The Faculty of Engineering is concerned with ensuring an environment that is free of all adverse discrimination. If there is a problem, that cannot be resolved by discussion among the persons concerned, individuals are reminded they should contact the Departmental Chair, the Sexual Harassment Officer or the Human Rights Consultant, as soon as possible."

"Academic dishonesty consists of misrepresentation by deception or by other fraudulent means and can result in serious consequences, e.g. the grade of zero on an assignment, loss of credit with a notation on the transcript (notation reads: 'Grade of F assigned for academic dishonesty'), and/or suspension or expulsion from the university.

It is your responsibility to understand what constitutes academic dishonesty. For information on the various kinds of academic dishonesty please refer to the Academic Integrity Policy, specifically Appendix 3, located at http://www.mcmaster.ca/policy/Students-AcademicStudies/AcademicIntegrity.pdf

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 Tuesday, March 26, 2019