G63.2855.001/G80.3042.004/G23.2855.001 -- Fall, 2007

Advanced Topics in Mathematical Physiology:

Computational Modeling of Neuronal Systems

Instructor: John Rinzel
Time: Thurs 9:30-11:20 am
Location: Warren Weaver Hall, Rm 1314
Prerequisites: familiarity with linear algebra, basic probability/statistics, differential equations. Some programming experience, e.g. matlab.

Brief Description:

We will survey various approaches to computational modeling of neuronal systems, from cellular to system level, from models of physiological mechanisms to more abstract models of information encoding and decoding. We will address the characterization of neuronal responses or identification of neuronal computations; how they evolve dynamically; how they are implemented in neural ware; and how they are manifested in human/animal behaviors. Modeling will involve deterministic and stochastic differential equations, information theory, and Bayesian estimation and decision theory.

Schedule:

Date Lecturer Topic Materials Homework
6 Sep J.Rinzel Intro to computational neuroscience: mechanistic vs. descriptive.
Nonlinear neuronal dynamics I: cellular excitability and oscillations
Course description/schedule
Reference chapter
Lecture slides
 
13 Sep J. Rinzel Nonlinear neuronal dynamics II: networks;
Case study: episodic activity in developing spinal cord
Lecture slides - Review
Lecture slides
HW 1
20 Sep E. Simoncelli Descriptive models of neural encoding I: linear/nonlinear cascade Lecture slides
Reference papers 1
Reference papers 2
 
27 Sep L. Paninski Neural encoding II: Fitting integrate-and-fire models to noisy spiking data Lecture slides
Reference papers 1
Reference papers 2
Reference papers 3
 
4 Oct E. Shea-Brown
J. Rinzel
Network models for decision making. Lecture slides (E S-B)
Lecture slides (JR)
Reference paper
 
11 Oct P. Glimcher Neurobiology of decision making Lecture slides
Reference paper
 
18 Oct N. Daw Reinforcement learning.
LOCATION (this lecture only): Rm 122, Center for Neural Science, 4 Washington Place
Lecture #1 slides
Lecture #2 slides
Reference papers 1
Reference papers 2
Reference papers 3
 
25 Oct T. Movshon Cortical processing of visual motion signals. Lecture slides
Reference paper
 
1 Nov N. Rubin / J. Rinzel Dynamics of perceptual bistability. JR Lecture slides
 
8 Nov A. Rangan Large-scale model of cortical area V1. Lecture slides  
15 Nov D. Tranchina Synaptic depression: from stochastic to rate model;
application to a model of cortical suppression.
Lecture slides
Reference paper
 
22 Nov No Class
[due to Thanskgiving]
     
29 Nov B. Pesaran Correlation between different brain areas. Lecture slides  
6 Dec A. Reyes Feedforward propagation in layered networks    
13 Dec Registered students Oral presentation of class projects    

Relevant Books:

  • Theoretical Neuroscience , by Dayan and Abbott. MIT Press, 2001.
  • Spikes: Exploring the Neural Code, by Rieke, Warland, de Ruyter, & Bialek. MIT Press, 1997.
  • Spiking Neuron Models: Single Neurons, Populations, Plasticity, by Gerstner and Kistler. Cambridge University Press, 2002.
  • Biophysics of Computation, by Koch. Oxford University Press, 1999.
  • Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, by Izhikevich. MIT Press, 2007.

    XPP codes for models:

    Hodgkin-Huxley XPP
    Morris-Lecar XPP
    Wilson-Cowan XPP

    Matlab codes for models:

    Hodgkin-Huxley Matlab
    FitzHugh-Nagumo Matlab