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
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
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.
Course notes
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.
| Final exam, 2007 | Final exam solutions 2007 |
| Final exam, 2006 | Final exam solutions 2006 |