Models of the Neuron (580.439/639)

Fall, 2007

Course overview

This course treats 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 goal of the course is understand how neurons work as biological computing elements and also to give students experience with modeling techniques as applied to complex biological systems.

The course meets Mondays and Wednesdays from 8:30-10:00 and Tuesdays from 9-10:00 at Homewood in Hodson 316. The MW classes are lectures and the T classes are recitations where homework will be discussed and help with Matlab provided; T classes are required for undergraduates and optional for graduate students. Occasional lectures will be given on Tuesday (see the detailed syllabus below). Taught by Eric Young, 505 Traylor at the Medical School, telephone 410-955-3164 (eyoung@jhu.edu); the T.A. is Abhishek Rege, telephone 410-955-0077 (arege@jhu.edu). Office hours will be Monday evening 4-6 in Clark 213. The prerequisites are mathematics through linear algebra and differential equations and 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, although 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. 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. 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. H.R. Wilson, Spikes Decisions and Actions and S.H. Strogatz Nonlinear Dynamics and Chaos cover aspects of nonlinear dynamics and network theory that will be discussed in the course. Additional references on network theory include J. Hertz, A Krogh, and R.G. Palmer Introduction to the Theory of Neural Computation and P. Dayan and L.F. Abbott Theoretical Neuroscience. All of these are on reserve in Eisenhower library.

Weekly homework assignments will be given. Solutions should be handed in and will be 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%). Undergraduates will have the option of doing the second modeling project for extra credit, and their grade 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 Aug 06, 2007

Parentheses indicates no class meeting on a Monday or Wednesday. 
Tuesday lectures are in boldface
Monday/Wednesday lectures begin at 8:30, Tuesday lectures begin at 9:00. All lectures in Hodson 316.

Sep. 10, 12  Introduction; review of neurophysiology and thermodynamics; equilibria, electrodiffusion.

        17, 19  I-V relationships, cellular steady state; biological membranes and channels.

        24, 26  Barrier models of channel permeation; selectivity, independence.

Oct. 1, 3  Voltage clamp analysis; gating; Hodgkin-Huxley and other models.

        8, 9, 10  Phase-plane analysis of nonlinear systems, model reduction,  equilibrium points, linearization, classification of behavior near equilibrium points. The Tuesday lecture covers simulation methods.

        (15), 17  (Fall break),  Limit cycles, bursting.

        22, 24  Varieties of channels; role of calcium; neuromodulation.

Oct. 29, 31  MIDTERM EXAM ON OCT 29, 2007. Examples: corticothalamic neurons; regulation of ion channel density.

Nov.  5, 7  Cable equation, finite cylinders, the equivalent cylinder.

FIRST MODELING PROJECT DUE NOV 12, 5:00 P.M.

        12, 14  Rall motorneuron model; dendritic tree inverse problems; compartmental models.

        19, 21  Real dendritic trees, synaptic coupling to the soma, arrangement of synapses.

        26, 28  Spines and calcium; plasticity; feedforward and recurrent neural networks.

Dec. 3, 5  Stability of network fixed points; network dynamics.

        10  Liapunov functions and the Cohen-Grossberg theorem.

Dec. 18  FINAL EXAM 9-12 AM.

SECOND MODELING PROJECT DUE DEC 21, 5:00 P.M.


Homeworks

Homework assignments will be given weekly, and are generally due on Wednesdays by 5:00pm. They can be submitted in class or dropped off in the homework mailbox (Clark Hall Rm. 318). Homework will not be accepted after solutions are posted. The links below will return pdf files of the homework sets and solutions. The pdf files can be viewed with the free Adobe Acrobat Reader. Solution sets will be available for downloading after the due-date of the homework.

Homework 1
Solutions to Homework 1

Homework 2

Solutions to Homework 2

Homework 3

Solutions to Homework 3

Homework 4

Solutions to Homework 4

Homework 5

Solutions to Homework 5 

Homework 6

Solutions to Homework 6 

Homework 7

Solutions to Homework 7 

Homework 8

Solutions to Homework 8 

Homework 9

Solutions to Homework 9 


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
  6. Papers on Dendritic Processing

Class lectures


Other relevant notes


Modelling projects

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

Project 1 : DUE MONDAY (NOVEMBER 12), 5:00 P.M.
Please download the following to get started :
Instructions/Description/Assignment
Supporting Codes
Grading - Project 1 Stats.
Note : Solutions will NOT be put online. Please contact Abhishek with questions pertaining to grading scheme and partial credit.

Project 2 : DUE FRIDAY (DECEMBER 21), 5:00 P.M.
Please read the following to get started :
Instructions/Description/Suggestions
Project Proposal Due on NOVEMBER 26




Previous exams

Endterm 2007
Solutions to Endterm 2007
Averages, Standard Deviations


Midterm 2007
Solutions to Midterm 2007
Grading Scheme
Averages, Standard Deviations
Please see Abhishek during office hours on Monday
in case of any discrepancies.

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

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, 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