Math 3375: Computational Neuroscience

Winter Semester '07, Dr. Rubin

General Class Information

• Class Meetings: M 12:30-1:50 PM and R 10:30-11:50 AM, BENEDUM 920
• Instructor: Jonathan Rubin

  Tentative Office Hours: Mon. 2:00-3:30 PM, Wed. 12:00-1:30 PM, and by appointment
  Office: Thackeray 504
  Phone: 624-6157
  EMAIL: rubin(at)math(dot)pitt(dot)edu
  WWW: http://www.math.pitt.edu/~rubin

  Text: Theoretical Neuroscience by Peter Dayan and L.F. Abbott

  Course reserves available in Thackeray Hall, 4th floor library:

  Theoretical Neuroscience, by P. Dayan and L.F. Abbott
  Introduction to Theoretical Neuroscience, by H. Tuckwell
  Foundations of Cellular Neurophysiology, by D. Johnston and S.M. Wu
  Methods in Neuronal Modeling, ed. by C. Koch and I. Segev
  Nonlinear Dynamics and Chaos, by S. Strogatz
  Dynamical Systems in Neuroscience, by E. Izhikevich (coming)

  Additional Useful Texts:

  • Brain Facts from the Society for Neuroscience
  • Johnston, D. & Wu, S., (1994) Foundations of cellular neurophysiology. Cambridge MA: MIT Press
  • Kandel, E. R., Schwartz, J. H. & Jessell, T. M. (1991) Principles of Neural Science. New York: Elsevier.
  • Koch, C & Segev, I (1998) Methods in neuronal modeling: From synapses to networks. Cambridge MA: MIT press (2nd edition).

Grading

Some useful links

• Center for Neuroscience at Pitt (CNUP)
• Center for the Neural Basis of Cognition (CNBC)
• Pubmed
• Digital brain anatomy
• Computational Neuroscience on the web
• MathSciNet

Note: all sections refer to the Dayan and Abbott text unless otherwise indicated.

• 1/4/07-1/11/07: Introduction; the passive patch (of neuronal membrane) and the equivalent circuit representation (5.1-5.3); review of some mathematical basics.
  • nice illustration of a neuron, from Brain Facts by the SFN.
  • Herz et al., Science article on different types of neuronal models.
  • XPPAUT on Bard Ermentrout's website.
  • Homework Assignment #1.
  • Addendum to Homework Assignment #1.
• 1/18/07-1/29/07: Propagation of potential along a passive neuronal cable and multi-compartment models (6.3-6.4)
• 2/1/07-2/8/07: Integrate-and-fire and other highly simplified single-compartment neuronal models (5.4); review of phase portraits
  • Homework Assignment #2.
  • Izhikevich 2003 paper w/matlab code.
  • Izhikevich 2004 paper.
  • Section 8.1 from Izhikevich, 2007.
• 2/12/07-3/2/07: Voltage-dependent conductances, conductance-based models, and simplifications (5.2,5.3); Morris-Lecar model
  • Hodgkin and Huxley, J. Physiol. (1952) 117(4):500-544.
  • A random example of recent work on the HH model with synaptic connections.
  • Channeling with Bard Ermentrout. NOTE: for some reason, ps2pdf inverted the page order (i.e., this goes from pg. 10 down to pg. 1).
  • Channeling with Bard - exploring the HH equations.
  • Voltage clamp experiment.
  • Studying the roles of different currents.
  • Zoo of models: XPPAUT files.
  • Ermentrout/Rinzel Chapter on Morris-Lecar plus phase planes and bursting.
• 3/12/07-3/22/07: Stochastic channels (5.7), synaptic conductances and short-term plasticity (5.8), synaptically coupled cells and network models (5.9, Chapter 7). Homework assignment 3, due Thursday, March 22nd. Three models of short-term synaptic plasticity:
  • Bose, Manor, Nadim, 2001.
  • Abbott et al., 1997.
  • Tsodyks and Markram, 1997.
  Links for homework assignment:
  • Problem 1, parts 1-5.
  • Problem 2, parts 1-4.
  Scanned pdf from Van Vreeswijk et al., 1994.
• 3/26/07-4/2/07: Firing rate models (Chapter 7). Homework assignment 4, due Thursday, April 19th.
  • Brody, Romo, Kepecs, 2003 on graded persistent activity.
• 4/2/07-4/9/07: Neural encoding (topics from Chapters 1 and 2.1,2.2)
• 4/12/07-4/19/07: Principal components analysis and a bit of information theory; a few words on plasticity and learning rules
  coding papers:
  • Borst and Theunissen, Nat. Neurosci., 1999 intro to information theory and neural coding
  • Juusola and French, Neuron, 1997 using SNR to compute mutual information
  • Petersen et al., J. Neurosci., 2002 information in barrel cortex

STDP papers:
• Song and Abbott, Neuron, 2001 cortical remapping with STDP
• Rubin, Lee, Sompolinksy, PRL, 2001 on additive vs. multiplicative (saturating) STDP
• Karbowski and Ermentrout, PRE, 2002 a nice phenomenological STDP model
• Izhikevich and Desai, Neural Comp., 2003 short paper on STDP and BCM
• Chechik, Neural Comp., 2003 a link between STDP and information theory