IMA New Directions
Jonathan E. Rubin's References
for the New Directions Short Course
June 16-27, 2008
DAY 1: June 16, 2008 – Introduction
to the Nervous System
3) M.C. Diamond, A.B. Scheibel, L.M. Elson, ``The Human Brain
Book'', 1985, HarperCollinsPublishers, New York, NY
4) "Principles of Neural Science", edited by E. Kandel et al.
5) J. Lubke, V. Egger, B. Sakmann, and D. Feldmeyer, "Columnar
of dendrites and axons of single and synaptically coupled
spiny neurons in layer 4 of the rat barrel cortex", J.
6) A. Gupta, Y. Wang, and H. Markram, "Organizing principles
diversity of GABAergic interneurons and synapses in the
Science, 287:273–278, 2000.
7) H. Markram, M. Toledo-Rodriguez, Y. Wang, A. Gupta, G.
C. Wu, "Interneurons of the neocortical inhibitory system",
Neurosci., 5:793–807, 2004.
DAY 2: June 17, 2008 – Simple
Models and Networks
1) A.V.M. Herz et al., Modeling Single-Neuron Dynamics and
Computations: A Balance of Detail and Abstraction, Science,
2) E.M. Izhikevich, Simple Model of Spiking Neurons, IEEE
Neural Networks, 14:1569–1572, 2003.
3) E.M. Izhikevich, Which Model to Use for Cortical
IEEE Trans. Neural Networks, 2004.
4) J. Keener, F. Hoppensteadt, and J. Rinzel,
models of nerve membrane response to oscillatory input, SIAM
5) S. Coombes and P. Bressloff, Mode-locking and Arnold
integrate-and-fire neural oscillators, Phys. Rev. E
6) P. Bressloff, Lectures in Mathematical
Series (AMS), 2008.
7) E. Izhikevich, Dynamical Systems in Neuroscience: The Geometry
Excitability and Bursting (2006), MIT Press, Cambridge, MA.
DAY 3: June 18, 2008 –
Hodgkin, A., and Huxley, A. (1952): A quantitative description
current and its application to conduction and excitation in
Johnston, D., and Wu, S. (1997): Foundations of Cellular
MIT Press, Cambridge, MA.
Dayan, P., and Abbott, L. (2001): Theoretical Neuroscience, MIT
Kepler, T.B., Abbott, L.F. and Marder, E. (1992) Reduction of
Conductance-Based Neuron Models. Biol. Cybern. 66: 381–387.
Troy, William C. The bifurcation of periodic solutions in the
Hodgkin-Huxley equations. Quart. Appl. Math. 36 (1978/79),
DAY 4: June 19, 2008 – Membrane
Dynamics, Singular Perturbation, Bursting, Synapses
J. Drover, J. Rubin, J. Su, and B. Ermentrout, Analysis of
mechanism by which excitatory synaptic coupling can synchronize
low firing frequencies, SIAM J. Appl. Math., 65:69–92, 2004.
J. Su, J. Rubin, and D. Terman, Effects of noise on
bursters, Nonlinearity, 17:133–157, 2004.
J. Rubin, Surprising effects of synaptic excitation, J.
Comp. Neurosci., 18:333–342, 2005.
J.Rubin and M. Wechselberger, Giant squid-hidden canard:
geometry of the Hodgkin-Huxley model, Biol. Cybern.
J.Rubin and M. Wechselberger, The selection of mixed-mode
oscillations in a Hodgkin-Huxley model with multiple
E. Lee and D. Terman, Uniqueness and stability of periodic
solutions, J. Diff. Equations, 158:48–78, 1999.
E.M. Izhikevich, Neural excitability, spiking and
bursting, Int. J.
Bif. Chaos, 10:1171–1266, 2000.
Rinzel, J. Bursting oscillations in an excitable membrane
and partial differential equations (Dundee, 1984), 304–316,
Notes in Math., 1151, Springer, Berlin, 1985.
Rinzel, John A formal classification of bursting mechanisms in
systems. Proceedings of the International Congress of
Vol. 1, 2 (Berkeley, Calif., 1986), 1578–1593, Amer. Math.
Providence, RI, 1987.
Rinzel, J. A formal classification of bursting mechanisms in
systems. Mathematical topics in population biology,
neurosciences (Kyoto, 1985), 267–281, Lecture Notes in
Springer, Berlin, 1987.
M. Pedersen and M. Sorensen, The effect of noise on beta-cell
period, SIAM J. Appl. Math, 67: 530–542, 2007.
Terman, D. The transition from bursting to continuous spiking
membrane models. J. Nonlinear Sci. 2 (1992), no. 2,
Terman, David Chaotic spikes arising from a model of bursting
membranes. SIAM J. Appl. Math. 51 (1991), no. 5,
J. Best, A. Borisyuk, J. Rubin, D. Terman and M. Wechselberger,
dynamic range of bursting in a model respiratory pacemaker
J. Appl. Dyn. Syst., 4: 1107–1139, 2005.
G.S. Medvedev, Reduction of a model of an excitable cell to a
one-dimensional map, Physica D, 202(1–2), 37–59, 2005.
DAY 5: June 20, 2008 – Small
Networks and Synchrony
J. Rubin and D. Terman, Geometric analysis of population
synaptically coupled neuronal networks, Neural Comp.,
J. Rubin and D. Terman, Analysis of clustered firing
synaptically coupled networks of oscillators, J. Math. Biol.,
J. Rubin, Bursting indcued by excitatory synaptic coupling
nonidentical conditional relaxation oscillators or square-wave
Phys. Rev. E, 74:021917, 2006.
Jonathan Rubin and David Terman, "Geometric Singular
of Neuronal Dynamics," in B. Fiedler, editor, Handbook of
Systems, Vol. 2, Elsevier, 2002.
D. Somers and N. Kopell, "Rapid synchronization through fast
modulation", Biol. Cybern. 68 (1993), 393–407.
D. Somers and N. Kopell, "Waves and synchrony in arrays of
relaxation and non-relaxation type", Physica D 89 (1995)
D. Terman, N. Kopell and A. Bose, ``Dynamics of two mutually
neurons'' Physica D 117:241–275 (1998).
J. Rubin, "Bursting induced by excitatory synaptic coupling in
non-identical conditional relaxation oscillators or square-wave
Phys. Rev. E, 74, 021917, 2006.
DAY 8: June 25, 2008 – Synaptic
L.F. Abbott et al., Synaptic depression and cortical gain
Science 275:221–224, 1997.
M. Tsodyks and H. Markram, The neural code between
pyramidal neurons depends on neurotransmitter release
Nat. Acad. Sci. USA, 94:719–723, 1997.
J. Trommershauser, J. Marienhagen, and A. Zippelius,
of central synapses: slow diffusion of transmitter interacting
spatial distributed receptors and transporters, J. Theor.
M.C.W. van Rossum, G.Q. Bi, and G.G. Turrigiano, Stable
learning from spike-timing-dependent plasticity, J. Neurosci.,
A. Bose, Y. Manor, and F. Nadim, Bistable oscillations
synaptic depression, SIAM J. Appl. Math., 62:706–727, 2001.
J. Rubin, D. Lee, and H. Sompolinsky, Equilibrium
temporally asymmetric Hebbian plasticity, Phys. Rev. Lett.,
J. Rubin, R. Gerkin, G. Bi and C. Chow, Calcium time
course as a
signal for spike-timing-dependent plasticity, J.
Q. Zou and A. Destexhe, Kinetic models of spike-timing
plasticity and their functional consequences in detecting
Biol. Cybern., 2008.
B. Earnshaw and P. Bressloff, Modeling the role of lateral
diffusion in AMPA receptor trafficking along a spiny dendrite,
Neurosci., DOI10.1007/s10827-008-0084-8, 2008; see also
Earnshaw, Phys. Rev. E, 2007 and Bressloff, Earnshaw and Ward,
Appl. Math, 2007, referenced in the Earnshaw and Bressloff
A. Destexhe, Z. Mainen and T. Sejnowski, Synthesis of models
membranes, synaptic transmission and neuromodulation using a
kinetic formalism, J. Comput. Neurosci., 1: 195–231, 1994.
S. Song, K. Miller and L. Abbott, Competitive Hebbian learning
spike-timing-dependent synaptic plasticity, Nat. Neurosci.
Song, S. and Abbott, L.F. (2001) Column and Map Development and
Re-Mapping Through Spike-Timing Dependent Plasticity. Neuron
L. Abbott and W. Regehr, Synaptic computation, Nature
J. Karbowski and G.B. Ermentrout, Synchrony arising from a
synaptic plasticity in a network of heterogeneous neural
Phys. Rev. E, 65:031902, 2002.
DAY 9: June 26, 2008 – Waves,
Evans Functions, Spatial Models
DAY 10: June 27, 2008 –
Development, Pattern Formation
Y. Guo, J. Rubin, C. McIntyre, J. Vitek, and D. Terman,
"Thalamocortical relay fidelity varies across subthalamic
brain stimulation protocols in a data-driven computational
Neurophysiol., 99: 1477–1492, 2008.
J. Rubin and K. Josic, "The firing of an excitable neuron in
presence of stochastic trains of strong inputs", Neural Comp.,
Jonathan Rubin and David Terman, "High frequency stimulation of
subthalamic nucleus eliminates pathological rhythmicity in a
computational model," J. Comp. Neurosci., 16: 211–235, 2004.
D. Terman, J.E. Rubin, A.C. Yew and C.J. Wilson, "Activity
a model for the Subthalamopallidal Network of the Basal
Neurosci., 22: 2963–2976, 2002.