Computational Neuroscience
Spring 1998
Bard Ermentrout
Walt Schneider
Coordinates:
- Lectures:
- Wed 12:30 PM - 1:50 PM Benedum 1222
- Thur 11:00 AM - 12:30 PM Cathedral of Learning 237
Instructors:
Bard
Ermentrout
Walt Schneider
Abstract
The course offers an introduction to modeling methods in neuroscience. It
illustrates how models can extend and evaluate neuroscience concepts.
Basic techniques of modeling biophysics, excitable membranes, small network
and large scale network systems will be introduced. The course begins with
a consideration of mathematical models of excitable membranes, including
the Hodgkin-Huxley model and simplifications such as the Morris-Lecar and
FitzHugh-Nagumo models. It will provide hands-on laboratory experience in
modeling membranes, neurons, and neural networks. The course explores the
use of differential equations, numerical simulation, and graphical
techniques for modeling compartmental and connectionist neural systems.
The range of topics include simulations of electrical properties of
membrane channels, single cells, neuronal networks and connectionist
simulation. Students will be afforded laboratory experience in computer
modeling, and they will develop computational neuroscience models in the
course. Prerequisites for the course include basic knowledge of calculus,
neuroscience, and some computer programming.
Required texts: None
Recommended Texts:
- Bower, J. M. & Beeman, D. (1995) The Book of GENESIS New York
Springer-Verlag.
- Johnston, D. & Wuu, S., (1994) Foundations of cellular neurophysiology.
Cambridge MA: MIT Press20
- Kandel, E. R., Schwartz, J. H. & Jessell, T. M. (1991) Principles of Neural
Science. New York: Elsevier.
- Koch, C & Segev, I (1989) Methods in neuronal modeling: From synapses to
networks. Cambridge MA: MIT press (paper back edition).
- Shephard, G. M. (1990) The synaptic organization of the brain New York:
Oxford University Press. (paper back edition)
- White, E. L. (1989) Cortical Circuits: Synaptic organization of the cerebral
cortex structure, function, and theory. Boston: Birkhauser,
Syllabus
- Goals and Math review ( E) 1-2 class periods
- Why model
- What you learn
- Levels of modeling
- Don't view simulators as black boxes
- Getting intuition as to what the models will do
- How to translate behavior into ODE
- Math Review
- Review of linear odes
- Review of matrices and eigenvalues
-
Optional info on xpp and linear/nonlinear diffeqs
- Passive Membrane (E) 2 periods
Optional Readings: Chap. 5 B& B; handouts
- Introduction
- compartment
- dendrites
- resting potentials
- cable
- Modeling passive membranes (Chap. 3 B&B)
- equations for single compartment
- multi-compartment model
- cable theory
- Computer implementation (E & S) 4 periods
- UNIX workshop for students not used to UNIX (Handouts) (special session)
- operating in UNIX
- editing
- simulation methodology
- phaseplane simulation environment (handouts)
- branching structure of a dendrite Genesis cable and two neurons (Chap.
2,3,10-12 B&B)
- Active membranes basics (E & S) 3 periods
{Readings: Rinzel & Ermentrout Chap. 5 K&S; Chap. 4 B& B; handouts}
- Synapses 2 periods
{Readings: Chap. 6,McCormick Chap.2 in Shepherd 1990}
- Channels
- model basics
- Kinetic theory (Mainen and Sejnowski)
- GABA_A vs GABA_B
- second messengers
- Multiple levels of simulation
- Numeric approximation
- Simulating channel effects
- Example models Brown, others
- Full cell simulation (E & S) 1 period
{Readings: K&S Chap. 4; Chap. 14 B&B}
- Implementing multiple channels
- Determining empirical parameters
- Modeling the cortical microcircuit
- Population modeling (S) 2 periods
{ Readings Wilson & Bower Chap. 9 K&S; Chap. 17 B&B; Chap. 3&4 White;
Douglas & Martin 1992) }
Please grab this lengthy paper for the next
several lectures.
- Simplifying systems
- specialization
- receptive fields
- columns
- regions
- laminar distribution
- Identifying cell types
- Building up the system
- Interconnecting cells
- Examining population behavior
- Try these little networks!
- CLASS EXAM 1 period
- Here are the exam odes EXAM1.ODE and
EXAM2.ODE
- Simplified biological modeling
- Population activity in barrel fields (Dan Simons) 1 period
- using biological input and outputs
- problems of scaling
- how much and what kind of detail
- Connectionist modeling with a biological interest (Jay McClelland David
Plaut) 5 periods
- Introduction to PDP: philosophy, framework learning rules: Hebb, comp.
learn, contrast Hebb, BP relation biological synaptic modification
- Perception and models of perception/attentional disorders
- interactive activation model, stochastic version
- relation to Zipser's work relating network to neural variables
- Mosher & Behrmann and other models of neglect and other phenomena
- Development, language acquisition, language processing
- why PDP central to not only biological but also functional issues in
development
- Hebbian models of biological development (Linsker, Miller, etc.)
- PDP models of cognitive and language development and interpretation of
developmental and acquired disorders of reading and language
- Role of hippocampus in learning and memory. (Gluck, Myers, Schmajuk,
DiCarlo & others)
- Testing models (E & S)
- Getting parameters from the empirical data
- Prediction of basic effects and robustness
- acceptance criteria
- predictions of model
- sensitivity analysis
- Neuron Simulators (S)
- Neuron 2 periods
- single cell simulation
- small networks
- Genesis 1 periods
- general nature of the tool
- Other models
- Role of Simulation versus analysis
- conceptualization benefits
- computational benefits
- REVIEW SESSION 1 period
- IN CLASS Final 1 period
- Projects