Systems Computational Neuroscience (Math 636)

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Readings

One- and two-dimensional neural systems
I: Chapter 3

I: Chapter 4

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Bursting
I: Chapter 9

R. J. Butera, J. Rinzel & J. C. Smith (1999), 'Models of respiratory rhythm generation in the pre-Botzinger complex. I. Bursting pacemaker neurons', J. Neurophysiol. 82:382-397.

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Chemical and electrical synapses / Synaptic transmission
J&W: Chapter 11

J&W: Chapter 12

J&W: Chapter 13

D&A: Chapters 5.8 & 5.9

A. Destexhe, Z. F. Mainen & T. J. Sejnowski (1998), 'Kinetic models of synaptic transmission'. In 'Methods in Neural Modeling', 2nd Edition, C. Koch and I. Segev (Eds.), MIT Press.

D. Terman & B. Ermentrout. Computational Neuroscience. Chapter 7.

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Membrane potential (sub-threshold) and firing frequency (supra-threshold) resonance

B. Hutcheon & Y. Yarom (2000), 'Resonance, oscillation and the intrinsic frequency preferences of neurons', Trends Neurosci., 23:216-222

T. A. Engel, L. Schimansky-Geier, A. V. M. Herz, S. Schreiber and I. Erchova (2008), 'Subthreshold Membrane-Potential Resonances Shape Spike-Train Patterns in the Entorhinal Cortex', J. Neurophysiol. 100:1576-1589

M. J. E. Richardson, N. Brunel, V. Hakim (2003), 'From Subthreshold to Firing-Rate Resonance', J. Neurophysiol. 89:2538-2554

Z. F. Mainen & T. J. Sejnowski (1995), 'Reliability of spike timing in neocortical neurons', Science, 268:1503-1506

S. Schreiber, I. Samengo & A. V. M. Herz (2009), 'Two distinct mechanism shape the reliability of neural responses', J. Neurophysiol 101:2239-2251

G. Mato & I. Samengo (2008), 'Type I and type II neuron models are selectively driven by differential stimulus features' Neural Computation' 20:2418-2440.

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Phase Response Curves / Spike Time Response Curves

D. Terman & B. Ermentrout. Computational Neuroscience. Chapter 8.

C. C. Canavier (2006), 'Phase response curve', Scholarpedia, 1(12):1332.

C. Acker, J. A. White & N. Kopell (2003), 'Synchronization of strongly coupled excitatory neurons: relating network behavior to biophysics', J. Comp. Neurosci., 15:71-90.

D. D. Pervouchine, T. I. Netoff, H. G. Rotstein, J. A. White, M. O. Cunningham, M. A. Whittington, N. J. Kopell (2006), 'Low-dimensional maps encoding dynamics in entorhinal cortex and hippocampus'

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Central Pattern Generators

E. Marder & R. L. Calabrese (1996), 'Principles of Rhythmic Motor Pattern Generation', Physiological Reviews, 687-717

R. M. Ghigliazza & P. Holmes (2004), 'A minimal model of a central pattern generator and motoneurons for insect locomotion', SIAM J Applied Dynamical Systems, 3:671-700

C. Soto-Trevino, P. Rabbah, E. Marder & F. Nadim (2005), 'Computational Model of Electrically Coupled, Intrinsically Distinct Pacemaker Neurons', J Neurophysiol 94:590-604

J.-M. Ramirez, A. K. Tryba, F. Pena (2004), 'Pacemaker neurons and neuronal networks: an integrative view', Current Opinion in Neurobiology, 14:665-674

A. Taylor, G. W. Cotrell, W. B. Kristan (2000),'A model of the leech segmental swim central pattern generator', Neurocomputing 32-33:573-584

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Data Analysis (Jaime de la Rocha)

Introduction to the Analysis of Neuronal Data: spike trains

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Networks

D. Terman & B. Ermentrout. Computational Neuroscience. Chapter 9.

B. Ermentrout (1998) 'Phase-Plane Analysis of Neural Nets'

F. K. Skinner, N. Kopell, E. Marder (1994), 'Mechanisms for Oscillation and Frequency Control in Reciprocally Inhibitory Model Neural Networks' J. Comp. Neurosci., 1:69-87

D. Terman, N. Kopell & A. Bose (1998), 'Dynamics of two mutually coupled slow inhibitory neurons', Physica D 117:241-275.

N. Kopell & D. Somers (1995), 'Anti-phase solutions in relaxation oscillators coupled through excitatory interactions', J. Math. Bio. 33:261-280

C. van Vreeswijk, L. F. Abbott, G. B. Ermentrout (1994), 'When Inhibition not Excitation Synchronizes Neural Firing', J. Comp. Neurosci., 1:313:321.

K. Senn, J. C. Jorge-Rivera, E. Marder, L. F. Abbott (1996), 'Decoding Synapses', J. Neurosci., 16:6307-6318.

F. Nadim, Y. Manor, N. Kopell, E. Marder(1999), 'Synaptic depression creates a switch that controls the frequency of an oscillatory input', PNAS, 96:8206-8211.

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Waves

B. Ermentrout & D. Pinto (2007), 'Neurophysiology and waves', SIAM News, Vol 40

D. Golomb, X.-J. Wang, J. Rinzel (1996), 'Propagation of spindle waves in a thalamic slice model', J. Neurophysiol, 75:750-769

A. Devor & Y. Yarom (2002), 'Generation and Propagation of Subthreshold Waves in a Network of Inferior Olivary Neurons', J Neurophysiol 87:3059-3069

O. Feinerman, M. Segal & e. Moses (2005), 'Signal Propagation Along Unidimensional Neuronal Networks', J Neurophysiol, 94:3406-3416

D. J. Pinto, S. L. Patrick, W. C. Huang & B. W. Connors, 'Initiation, Propagation, and Termination of Epileptiform Activity in Rodent Neocortex In Vitro Involve Distinct Mechanisms', J. Neurosci. 25:8131-8140

X. Huang, W. C. Troy, Q. Yang, H. Ma, C. R. Laing, S. J. Schiff & J.-Y. Wu (2004), 'Spiral Waves in Disinhibited Mammalian Neocortex', J. Neurosci 24:9897:9902

R. Osan & B. Ermentrout (2002), 'The evolution of synaptically generated waves in one- and two-dimensional domains', Physica D 163:217-235

R. Osan, J. Rubin & B. Ermentrout (2002), 'Regular traveling waves in a one-dimensional network of theta neurons', SIAM J Appl. Math 62:1197-1221

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Rate Equations (.ode)

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Matlab - Basics (D. Kim & J. Yi)

Notes

m-file 1 - m-file 2 - m-file 3 - m-file 4

Books

T&E : "Mathematical Foundations of Neuroscience", by G. B. Ermentrout & D. H. Terman - Springer (2010), 1st edition. ISBN 978-0-387-87707-5.

J&W : "Foundations of Cellular Neurophysiology", by Daniel Johnston and Samuel M.-S. Wu. The MIT Press, 1995. ISBN 0-262-10053-3.

I : "Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting", by Eugene M. Izhikevich. The MIT Press, 2007. ISBN 0-262-09043-8

K : "Biophysics of Computation - Information processing in single neurons", by Christof Koch. Oxford University Press, 1999. ISBN 0-19-510491-9.

D&A : "Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems", by Peter Dayan and Larry F. Abbott. The MIT Press,2001. ISBN 0-262-04199-5

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Department of Mathematical Sciences(DMS).

New Jersey Institute of Technology (NJIT).

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Horacio

Last modified: Fri Apr 30 17:40:33 EDT 2010