Models of the Neuron (580.439/639)

Fall 2014

Course overview

This course discusses single neuron modeling, including molecular models of channels and channel gating, Hodgkin-Huxley style models of membrane currents, non-linear dynamics as a way of understanding membrane excitability, neural integration through cable theory, and network computation. The goals of the course are to understand how neurons work as biological computing elements and to give students experience with modeling techniques as applied to complex biological systems.

The course meets Mondays, Wednesdays, and Fridays from 9:00-10:00 a.m. on the Homewood campus in Hodson 211. The MWF classes are lectures. There will also be a Tuesday recitation and homework-help class F 4:00 in Hodson 203; this is strongly recommended for all students. The course is taught by Eric Young, 505 Traylor at the Medical School, telephone 410-955-3164 ( Office hours are by arrangement. The prerequisites are mathematics through linear algebra and differential equations plus an introduction to neuroscience (e.g. 580.422, 080.205, or 080.304); introductory signal and system theory (e.g. 580.222 or 520.213-214) is helpful.

There is no required text. Instead readings will be assigned from the literature and from several of the following books. All the books are on reserve in the library. Biophysics of Computation by C. Koch is an excellent book that covers most of the material in the course. Foundations of Cellular Neurophysiology by D. Johnston and S. Wu covers some of the material in a more elementary fashion and P. Dayan and L.F. Abbott Theoretical Neuroscience provides a more modern view of some topics. Several chapters from Methods in Neuronal Modeling (2nd ed.) edited by C. Koch and I. Segev will be used. An excellent and comprehensive book on membrane physiology is Ionic Channels of Excitable Membranes, (3rd ed.) by B. Hille. This book covers ion channels in more depth than those above; it is required reading for anyone seriously interested in this subject. Additional references include the following: G.M. Shepherd, The Synaptic Organization of the Brain (4th ed.) is a good introduction to neural systems for persons with no previous experience. S.H. Strogatz Nonlinear Dynamics and Chaos cover aspects of nonlinear dynamics and network theory that will be discussed in the course; some material from H.R. Wilson, Spikes Decisions and Actions will also be used. The book Dynamical Systems in Neuroscience by E.M. Izhikevich provides a useful view of 2nd-order nonlinear systems of the type used in neuroscience. A good overview of network theory is J. Hertz, A Krogh, and R.G. Palmer, Introduction to the Theory of Neural Computation. Finally, J.J.B. Jack, D. Noble, and R.W. Tsien, Electric Current Flow in Excitable Cells contains detailed discussions of older work, especially useful for cable theory.

Weekly homework assignments will be given. Solutions should be handed in during class on the due date and will be loosely graded. Two computer modeling projects will be assigned during the term. The grade for graduate students will be based on the midterm (20%), final (30%), the modeling projects (40%), and the homework (10%). Undergraduate's grades will be based on the midterm (30%), first modeling project (30%), final (30%), and homework (10%). Students are encouraged to discuss homework problems with colleagues, but the final product that is handed in should be the student's own work. Modeling projects must be done individually. A conscientious homework record will contribute to raising marginal grades.

Course schedule Updated August 22, 2014

Lectures are MWF 9-10 in Hodson 211. Parentheses indicates no class meeting on that day. The problem session meets T at a time TBD.


Aug 29, Sep. 3, 5 - Introduction; review of neurophysiology and thermodynamics. Equilibria, electrodiffusion I-V relationships;

8, 10, 12 - Cellular steady state. Biological membranes, ion transporters, channels.

15, 17, 19 - Kcsa and similar channels. Barrier models of channel permeation. Kcsa permeation model.

22, 24, 26 - Transporter models, voltage clamp analysis, gating; Hodgkin-Huxley and similar models.

Sep. 29, Oct. 1, 3 - Phase-plane analysis of nonlinear systems; model reduction, linearization; classification of behavior near equilibrium points

6, 8, 10 - Simulation methods; limit cycles; bifurcations, bursting.

13, 15, 16, (17) - Role of calcium; varieties of channels. Corticothalamic neurons. Regulation of ion channel density.


20, 22, 24 – Midterm exam. Synaptic transmission and neuromodulation. Dendritic trees, distribution of inputs on dendrites.

27, 29, 31 - Cable equation for dendritic trees; solutions to the cable equation; finite cylinders.


Nov. 3, 5, 7 - Transfer functions in dendritic trees; Equivalent cylinder.

10, 12, 14 - Real dendritic trees, synaptic coupling to the soma, arrangement of synapses, subunits.

17, 19, 21 - Spines and calcium. Plasticity; neural integration.

(24, 26, 28) – No class, Thanksgiving

Dec.1, 3, 5 - Network learning rules; Hopfield network; Liapunov functions and the Cohen-Grossberg theorem.

FINAL EXAM  Sat. December 13, 2-5 P.M.



Homework assignments will be given weekly, and are generally due on Mondays by the end of class. They can be submitted in class emailed to Eric Young. Homework will not be accepted after solutions are posted. The links below will return pdf files of the homework sets and solutions. Solution sets will be available for downloading after the due-date of the homework.

Homework 1        solutions

Homework 2        solutions

Homework 3        solutions

Homework 4        solutions


Homework_5       solutions


Homework 6        solutions


Homework 7        solutions


Homework 8        solutions


Homework 9        solutions

Course notes

  1. Review of circuit theory and differential equations
  2. Thermodynamics and Transport
  3. Channels, Selectivity, and Permeation
  4. Nonlinear Dynamics and Hodgkin Huxley Equations
  5. Cable Theory

Class lectures (updated as the course goes on)

Other relevant notes

Modeling projects

Two computer modeling projects will be assigned. All work on the modeling projects must be done individually.


Project #1 : Due October 31, 2014 by 5:00 P.M.

     Assignment     MLE matlab files


Project #2 : Due December 19, 2014 by 5:00 P.M.



Previous exams

Copies of previous midterms and finals are posted below, along with solutions.

Midterm exam 2014

Midterm exam solutions 2014

Midterm exam, 2013

Midterm exam solutions 2013

Midterm exam, 2012

Midterm exam solutions 2012

Midterm exam, 2011

Midterm exam solutions 2011

Midterm exam, 2010

Midterm exam solutions 2010

Midterm exam, 2009

Midterm exam solutions 2009

Midterm exam, 2008

Midterm exam solutions 2008

Midterm exam, 2007

Midterm exam solutions 2007

Midterm exam, 2006

Midterm exam solutions 2006

Midterm exam, 2005

Midterm exam solutions 2005

Midterm exam, 2004

Midterm exam solutions 2004

Midterm exam, 2003

Midterm exam solutions 2003

Midterm exam, 2002

Midterm exam solutions 2002

Midterm exam, 2001

Midterm exam solutions 2001

Midterm exam, 2000

Midterm exam solutions 2000

Midterm exam, 1999

Midterm exam solutions 1999

Midterm exam, 1998

Midterm exam solutions 1998

Midterm exam, 1997

Midterm exam solutions 1997

Final exam, 2014

Final exam solutions 2014

Final exam, 2013

Final exam solutions 2013

Final exam, 2012

Final exam solutions 2012

Final exam, 2011

Final exam solutions 2011

Final exam, 2010

Final exam solutions 2010

Final exam, 2009

Final exam solutions 2009

Final exam, 2008

Final exam solutions 2008

Final exam, 2007

Final exam solutions 2007

Final exam, 2006

Final exam solutions 2006

Final exam, 2005

Final exam solutions 2005

Final exam, 2004

Final exam solutions 2004

Final exam, 2002

Final exam solutions 2002

Final exam, 2001

Final exam solutions 2001

Final exam, 2000

Final exam solutions 2000

Final exam, 1999

Final exam solutions 1999

Final exam, 1998

Final exam solutions 1998

Final exam, 1997

Final exam solutions 1997