Unit 1: Action Potential Generation and Simple Neural Circuits

D. W. Tank, Depts. of Molecular Biology and Physics
J. J. Hopfield , Dept. of Molecular Biology

David Tank's Power Point slides (converted to pdf format) - note that although David is giving four lectures, the slides are all contained in these three files.
David Tank's Slides #1 (pdf)
David Tank's Slides #2 (pdf)
David Tank's Slides #3 (pdf)

  Overview of nervous system organization and electrochemical signaling in neurons (Tank)  Purves et al, Neuroscience, 2nd edition, Chapters 1,2, Reserve APC/EEB/MOL 514
   The Hodgkin/Huxley model of the action potential (Tank)  
  • A. L. Hodgkin and A. F. Huxley. A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117:500-544 (1952).
  • A. L. Hodgkin. The Croonian Lecture: Ionic Movements and Electrical Activity in Giant Nerve Fibres, Proceedings of the Royal Society of London, Series B, Biological Sciences, 148(930):1-37 (1958).
  • D. Johnston and S. M-S. Wu. Foundations of Cellular Neurophysiology, Chapter 6, Reserve APC/EEB/MOL 514
  • 9/19
      Generalization of Hodgkin/Huxley and simplified models of spiking neurons (Tank)  
      Neural circuit models of persistent neural activity and short term memory (Tank)  
  • H. S. Seung, D. D. Lee, B. Y. Reis, and D. W. Tank. Stability of the Memory of Eye Position in a Recurrent Network of Conductance-Based Model Neurons. Neuron 26:259-271 (2000).
  • H. S. Seung, D. D. Lee, B. Y. Reis, and D. W. Tank. The autapse: a simple illustration of short-term analog memory storage by tuned synaptic feedback. Journal of Computational Neuroscience 9:171-85 (2000).
  • E. Aksay, G. Gamkrelidze, H. S. Seung, R. Baker, and D. W. Tank. In vivo intracellular recording and perturbation of persistent activity in a neural integrator. Nature Neuroscience 4:184- 93 (2001).
  • 9/26
      Action potential synchrony and its significance to neuron computation (Hopfield)  
  • J. J. Hopfield and C. Brody. What is a moment? "Cortical" sensory integration over a brief interval. Proc Natl Acad Sci USA. 97(25):13919-24 (2000).
  • J. J. Hopfield and C. Brody. What is a moment? Transient synchrony as a collective mechanism for spatiotemporal integration. Proc Natl Acad Sci USA. 98(3):1282-7 (2001).
  • C. D. Brody and J. J. Hopfield. Simple networks for spike-timing based computation. Preprint.
  • J. J. Hopfield and C. D. Brody. Simple networks and learning rules for spike-timing based computation: learning rules. Preprint.
  • Volume 24, Issue 1 of Neuron
  • W. Singer. Neuronal synchrony: a versatile code for the definition of relations? Neuron 24:49-65 (1999).
  • M. N. Shadlen and J. A. Movshon. Synchrony unbound: A critical evaluation of the temporal binding hypothesis. Neuron 24:67-77 (1999).
  • 10/1
     Action potential synchrony and its significance to neuron computation, continued (Hopfield)  

    Unit 2: Dynamics of Disease

    J.B. Plotkin, Program in Applied and Computational Mathematics, and Institute for Advanced Studies, Program in Theoretical Biology
    J. G. Dushoff, Dept. of Ecology and Evolutionary Biology
    A.L. Lloyd, Institute for Advanced Studies, Program in Theoretical Biology

    Copies of Joshua Plotkin's PowerPoint slides will be distributed in class.

    Jonathan Dushoff's Slides #1 (pdf)
    Jonathan Dushoff's Slides #2 (pdf)

       Introduction to the dynamics of disease (Plotkin)  
  • F. Brauer and C. Castillo-Chavez, Mathematical models in population biology and epidemiology, Reserve APC/EEB/MOL 514
  • R. M. May, ``Population Biology of Microparasitic Infections'', pp.405-442 of Mathematical Ecology, ed. Hallam and Levin, Reserve APC/EEB/MOL 514 (requested)
  • A. S. Perelson and G. Weisbuch, Immunology for Physicists , Rev. Mod. Physics, 69:1219--1267, 1997
  • H. W. Hethcote, The mathematics of infectious diseases SIAM Rev., 42:599--653, 2000.
  • R. Ross The Prevention of Malaria, E.P. Dutton and Co., 1910.
  • R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control, 1991. APC/EEB/MOL 514 (requested)
  • 10/8
       Stochastic dynamics of epidemics (Plotkin)  
  • I. Nasell On the time to extinction in recurrent epidemics. J. Roy. Statist. Soc. 61: 309-320 (1999).
  • 10/10
      Influenza dynamics and vaccination strategies (Plotkin)  
  • M. A. Nowak and R. M. May, Virus Dynamics, Reserve APC/EEB/MOL 514
  • J. B. Plotkin, J. Dushoff, S. A. Levin. Hemagglutinin sequence clusters and the antigenic evolution of influenza A. Proc. Nat. Acad. Sci. 99: 6263-6268 (2002).
  • V. Andreasen, J. Lin, and S. A. Levin. The dynamics of cocirculating influenza strains conferring partial cross-immunity. (1997) J. Math. Biol. 35: 825--842.
  • 10/15
       Multi-group models of epidemics (Dushoff)  
  • C. Castillo-Chavez, H. W. Hethcote, V. Andreasen, S. A. Levin, and W. M. Liu. Epidemiological models with age structure, proportionate mixing and cross-immunity. J. Math. Biol. 27: 233--258 (1989).
  • 10/17
       Global dynamics and stability (Dushoff)  
      Spatial heterogeneity in epidemic models (Lloyd)  
  • A. L. Lloyd and R. M. May. Spatial heterogeneity in epidemic models. J. Theor. Biol. 179: 1-11 (1996).
  • Unit 3: Intracellular Networks

    W. S. Bialek, Dept. of Physics

    Lectures to focus on the phototransduction network in rod visual receptors and the chemotaxis network in bacteria.

    Bill Bialek's Notes on Phototransduction - includes HW5 (pdf)

       Phototransduction 1 (Bialek)  
  • see Bill's notes on phototransduction for reading list
  • 10/29, 10/31
       FALL RECESS  
      Phototransduction 2 (Bialek)  
       Phototransduction 3 (Bialek)  
       Chemotaxis 1 (Bialek)  
      Chemotaxis 2 (Bialek)  
       Chemotaxis 3 (Bialek)  

    Unit 4: Spatial Patterns in Development

    E. C. Cox , Dept. of Molecular Biology
    S.Y. Shvartsman, Dept. of Chemical Engineering

    Stas Shvartsman's Lecture Notes
    Stas Shvartsman's Notes #1 (pdf)
    Stas Shvartsman's Notes #2 (pdf)

       What kinds of spatial patterns do we see and what needs to be explained? (Cox)  
  • J.H. Claxton. The determination of patterns with special reference to that of the central primary skin follicles in sheep. J. Theor. Biol. 7:302-317 (1964).
  • G.J. Mitchison and M. Wilcox. Rule governing cell division in Anabaena. Nature 239:110-111 (1972).
  • 11/26
       Order from disorder in simple systems, and patterns from prepatterns in complex systems (Cox)  
      Long range order in dynamical systems (Cox)  
  • G. von Dassow, E. Meir, E.M. Munro, and G.M. Odell. The segment polarity network is a robust developmental module. Nature 406:188-192, 2000. Supplemental notes (MSWord format).
  • R. Albert, H. Othmer. The topology and signature of the regulatory interactions predict the expression pattern of the segment polarity genes in Drosophila melanogaster preprint, to appear.
  • 12/5
       Microscopic origins of diffusion and transport (Shvartsman)  
  • M. Schnitzer. Theory of continuum random walks and application to chemotaxis., Phys. Rev. E 48:2553-2568, 1993.
  • M. A. Rivero, R. T. Tranquillo, H. M. Buettner, and D. A. Lauffenburger, Transport models for chemotactic cell populations based on individual cell behavior, Chemical Engineering Science, 44(12):2881-2897, 1989.
  • H. Meinhardt and A. Gierer, Pattern formation by local self-activation and lateral inhibition. BioEssays 22:753-760, 2000.
  • Ch 9 of Edelstein-Keshet, Mathematical Models in Biology, on reserve in library.
  • 12/10
       Cell communication mechanisms in development (Shvartsman)  
  • M. Freeman. Feedback control of intercellular signalling in development. Nature 408:313-319, 2000.
  • H. Othmer, B. Lilly, and J.C. Dallon. Pattern formation in a cellular slime mold In Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems, E. Doedel and L. S. Tuckerman, (eds.), IMA Proceedings, 119, 359-383, (2000)
  • 12/12
       Pattern formation is paracrine and autocrine networks (Shvartsman)