IMA New Directions
Program
Jonathan E. Rubin's References
for the New Directions Short Course
June 1627, 2008
DAY 1: June 16, 2008 – Introduction
to the Nervous System
1) faculty.washington.edu/chudler/facts.html
2) discovermagazine.com/2007/aug/unsolvedbrainmysteries/articleprint
3) M.C. Diamond, A.B. Scheibel, L.M. Elson, ``The Human Brain
Coloring
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
organization
of dendrites and axons of single and synaptically coupled
excitatory
spiny neurons in layer 4 of the rat barrel cortex", J.
Neuorsci.,
20:5300–5311, 2000.
6) A. Gupta, Y. Wang, and H. Markram, "Organizing principles
for a
diversity of GABAergic interneurons and synapses in the
neocortex",
Science, 287:273–278, 2000.
7) H. Markram, M. ToledoRodriguez, Y. Wang, A. Gupta, G.
Silberberg, and
C. Wu, "Interneurons of the neocortical inhibitory system",
Nat. Rev.
Neurosci., 5:793–807, 2004.
DAY 2: June 17, 2008 – Simple
Models and Networks
1) A.V.M. Herz et al., Modeling SingleNeuron Dynamics and
Computations: A Balance of Detail and Abstraction, Science,
314:80–85,
2006.
2) E.M. Izhikevich, Simple Model of Spiking Neurons, IEEE
Trans.
Neural Networks, 14:1569–1572, 2003.
3) E.M. Izhikevich, Which Model to Use for Cortical
Spiking Neurons?,
IEEE Trans. Neural Networks, 2004.
4) J. Keener, F. Hoppensteadt, and J. Rinzel,
Integrateandfire
models of nerve membrane response to oscillatory input, SIAM
J. Appl.
Math.,
41:503–517, 1981.
5) S. Coombes and P. Bressloff, Modelocking and Arnold
tongues in
integrateandfire neural oscillators, Phys. Rev. E
60:2086–2096, 1999.
6) P. Bressloff, Lectures in Mathematical
Neuroscience,
PCMI Lecture
Series (AMS), 2008.
7) E. Izhikevich, Dynamical Systems in Neuroscience: The Geometry
of
Excitability and Bursting (2006), MIT Press, Cambridge, MA.
DAY 3: June 18, 2008 –
HodgkinHuxley Theory
Hodgkin, A., and Huxley, A. (1952): A quantitative description
of membrane
current and its application to conduction and excitation in
nerve. J.
Physiol. 117:500–544.
Johnston, D., and Wu, S. (1997): Foundations of Cellular
Neurophysiology,
MIT Press, Cambridge, MA.
Dayan, P., and Abbott, L. (2001): Theoretical Neuroscience, MIT
Press,
Cambridge, MA.
Kepler, T.B., Abbott, L.F. and Marder, E. (1992) Reduction of
ConductanceBased Neuron Models. Biol. Cybern. 66: 381–387.
Troy, William C. The bifurcation of periodic solutions in the
HodgkinHuxley equations. Quart. Appl. Math. 36 (1978/79),
no. 1,
73–83.
DAY 4: June 19, 2008 – Membrane
Dynamics, Singular Perturbation, Bursting, Synapses
J. Drover, J. Rubin, J. Su, and B. Ermentrout, Analysis of
a canard
mechanism by which excitatory synaptic coupling can synchronize
neurons at
low firing frequencies, SIAM J. Appl. Math., 65:69–92, 2004.
J. Su, J. Rubin, and D. Terman, Effects of noise on
elliptic
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 squidhidden canard:
the 3D
geometry of the HodgkinHuxley model, Biol. Cybern.
97:5–32,
2007.
J.Rubin and M. Wechselberger, The selection of mixedmode
oscillations in a HodgkinHuxley model with multiple
timescales, Chaos,
18:015105, 2008.
E. Lee and D. Terman, Uniqueness and stability of periodic
bursting
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
model. Ordinary
and partial differential equations (Dundee, 1984), 304–316,
Lecture
Notes in Math., 1151, Springer, Berlin, 1985.
Rinzel, John A formal classification of bursting mechanisms in
excitable
systems. Proceedings of the International Congress of
Mathematicians,
Vol. 1, 2 (Berkeley, Calif., 1986), 1578–1593, Amer. Math.
Soc.,
Providence, RI, 1987.
Rinzel, J. A formal classification of bursting mechanisms in
excitable
systems. Mathematical topics in population biology,
morphogenesis and
neurosciences (Kyoto, 1985), 267–281, Lecture Notes in
Biomath., 71,
Springer, Berlin, 1987.
M. Pedersen and M. Sorensen, The effect of noise on betacell
burst
period, SIAM J. Appl. Math, 67: 530–542, 2007.
Terman, D. The transition from bursting to continuous spiking
in excitable
membrane models. J. Nonlinear Sci. 2 (1992), no. 2,
135–182.
Terman, David Chaotic spikes arising from a model of bursting
in excitable
membranes. SIAM J. Appl. Math. 51 (1991), no. 5,
1418–1450.
J. Best, A. Borisyuk, J. Rubin, D. Terman and M. Wechselberger,
"The
dynamic range of bursting in a model respiratory pacemaker
network," SIAM
J. Appl. Dyn. Syst., 4: 1107–1139, 2005.
G.S. Medvedev, Reduction of a model of an excitable cell to a
onedimensional 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
rhythms in
synaptically coupled neuronal networks, Neural Comp.,
12:597–645, 2000.
J. Rubin and D. Terman, Analysis of clustered firing
patterns in
synaptically coupled networks of oscillators, J. Math. Biol.,
41:513–545, 2000.
J. Rubin, Bursting indcued by excitatory synaptic coupling
in
nonidentical conditional relaxation oscillators or squarewave
bursters,
Phys. Rev. E, 74:021917, 2006.
Jonathan Rubin and David Terman, "Geometric Singular
Perturbation Analysis
of Neuronal Dynamics," in B. Fiedler, editor, Handbook of
Dynamical
Systems, Vol. 2, Elsevier, 2002.
D. Somers and N. Kopell, "Rapid synchronization through fast
threshold
modulation", Biol. Cybern. 68 (1993), 393–407.
D. Somers and N. Kopell, "Waves and synchrony in arrays of
oscillators of
relaxation and nonrelaxation type", Physica D 89 (1995)
169–183.
D. Terman, N. Kopell and A. Bose, ``Dynamics of two mutually
inhibitory
neurons'' Physica D 117:241–275 (1998).
J. Rubin, "Bursting induced by excitatory synaptic coupling in
nonidentical conditional relaxation oscillators or squarewave
bursters",
Phys. Rev. E, 74, 021917, 2006.
DAY 8: June 25, 2008 – Synaptic
Plasticity
L.F. Abbott et al., Synaptic depression and cortical gain
control,
Science 275:221–224, 1997.
M. Tsodyks and H. Markram, The neural code between
neocortical
pyramidal neurons depends on neurotransmitter release
probability, Proc.
Nat. Acad. Sci. USA, 94:719–723, 1997.
J. Trommershauser, J. Marienhagen, and A. Zippelius,
Stochastic model
of central synapses: slow diffusion of transmitter interacting
with
spatial distributed receptors and transporters, J. Theor.
Biol.,
198:101–120, 1999.
M.C.W. van Rossum, G.Q. Bi, and G.G. Turrigiano, Stable
Hebbian
learning from spiketimingdependent plasticity, J. Neurosci.,
20:8812–8821, 2000.
A. Bose, Y. Manor, and F. Nadim, Bistable oscillations
arising from
synaptic depression, SIAM J. Appl. Math., 62:706–727, 2001.
J. Rubin, D. Lee, and H. Sompolinsky, Equilibrium
properties of
temporally asymmetric Hebbian plasticity, Phys. Rev. Lett.,
86:364–367,
2001.
J. Rubin, R. Gerkin, G. Bi and C. Chow, Calcium time
course as a
signal for spiketimingdependent plasticity, J.
Neurophysiol.,
93:2600–2613, 2004.
Q. Zou and A. Destexhe, Kinetic models of spiketiming
dependent
plasticity and their functional consequences in detecting
correlations,
Biol. Cybern., 2008.
B. Earnshaw and P. Bressloff, Modeling the role of lateral
membrane
diffusion in AMPA receptor trafficking along a spiny dendrite,
J. Comput.
Neurosci., DOI10.1007/s1082700800848, 2008; see also
Bressloff and
Earnshaw, Phys. Rev. E, 2007 and Bressloff, Earnshaw and Ward,
SIAM J.
Appl. Math, 2007, referenced in the Earnshaw and Bressloff
paper
A. Destexhe, Z. Mainen and T. Sejnowski, Synthesis of models
for excitable
membranes, synaptic transmission and neuromodulation using a
common
kinetic formalism, J. Comput. Neurosci., 1: 195–231, 1994.
S. Song, K. Miller and L. Abbott, Competitive Hebbian learning
through
spiketimingdependent synaptic plasticity, Nat. Neurosci.
3:919–926,
2000.
Song, S. and Abbott, L.F. (2001) Column and Map Development and
Cortical
ReMapping Through SpikeTiming Dependent Plasticity. Neuron
32:339–350.
L. Abbott and W. Regehr, Synaptic computation, Nature
431:796–803, 2004.
J. Karbowski and G.B. Ermentrout, Synchrony arising from a
balanced
synaptic plasticity in a network of heterogeneous neural
oscillators,
Phys. Rev. E, 65:031902, 2002.
DAY 9: June 26, 2008 – Waves,
Evans Functions, Spatial Models
References (pdf)
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
nucleus deep
brain stimulation protocols in a datadriven computational
model", J.
Neurophysiol., 99: 1477–1492, 2008.
J. Rubin and K. Josic, "The firing of an excitable neuron in
the
presence of stochastic trains of strong inputs", Neural Comp.,
19:
1251–1294, 2007.
Jonathan Rubin and David Terman, "High frequency stimulation of
the
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
patterns in
a model for the Subthalamopallidal Network of the Basal
Ganglia," J.
Neurosci., 22: 2963–2976, 2002.
