NJIT_Math451H_Spring-2014

Methods of Applied Mathematics II

Math451H - Spring 2014

Class Notes

HGR

Preliminary comments
Introduction to Neuronal dynamics
Neuronal models: the passive membrane equation
Integrate-and-fire models
The Hodgkin-Huxley model
Synaptic connectivity

References (final project)
STG neuron models

Mathematical model of an identified stomatogastric ganglion neuron (F. Buchholtz, J. Golowasch, I. Epstein, E. Marder; J Neurophysiol, 1992)
Reduction of a channel-based model for a stomatogastric ganglion LP neuron (D. Golomb, J. Guckenheimer, S. Gueron; Biol Cybern, 1993)
How multiple conductance determine electrophysiological properties in a multicompartment model (A. Taylor, J.-M. Goaillard, E. Marder; J Neurosci, 2009)
Computational model of electrically coupled, intrinsically distinct pacemaker neurons (C. Soto-Trevino, P. Rabbah, E. Marder, F. Nadim (J Neurophysiol; 2005)

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Genetic Algorithms

Courtesy: David Fox (Nadim lab)

A fast and elitist multiobjective genetic algorithm: NSGA-II (K. Deb, A. Pratap, S. Agarwal, T. Meyarivan, IEEE Trans. Evol. Comp., 2002)
A fast elitist multiobjective genetic algorithm: NSGA-II (A. Seshadri)
Multiobjective optimization using nondominated sorting in genetic algorithms (N. Srinivas & K. Deb)

Recommended Reading and Matlab Code Samples

Stochastic Runge-Kutta algorithms

I. White Noise
II. Colored Noise erratum

Matlab Tutorial (Kohitij Kar, CMBN, Rutgers )

Matlab Tutorial
Solutions

ODE Examples - Matlab (Jon Guez, CMBN, Rutgers)

ODEexamples

Introduction to the Neurosciences:

J&W: Chapter 1

Passive Membrane Properties:
J&W: Chapter 2
Membrane Potential. Elmslie, K. S. (2001) Encyclopedia of Life Sciences. John Wiley & Sons, Elmslie, K. S. (2001) Encyclopedia of Life Sciences. John Wiley & Sons, http://www.mrw.interscience.wiley.com/emrw/9780470015902/els/article/a0000182

Integrate-and-Fire Neurons

D&A: Chapter 5.1-5.4

The Hodgkin-Huxley model

Hodgkin, A. L. and Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve - The Journal of Physioloty, 117, 500-544
Action Potential: Ionic Mechanisms. Elmslie, K. S. (2001) Encyclopedia of Life Sciences. John Wiley & Sons, Elmslie, K. S. (2001) Encyclopedia of Life Sciences. John Wiley & Sons, http://www.mrw.interscience.wiley.com/emrw/9780470015902/els/article/a0000002
J&W: Chapter 6
I: Chapter 2

The cable equation

Passive Propagation of Electrical Signals. Elmslie, K. S. (2005) Encyclopedia of Life Sciences. John Wiley & Sons, Elmslie, K. S. (2005) Encyclopedia of Life Sciences. John Wiley & Sons, http://www.mrw.interscience.wiley.com/emrw/9780470015902/els/article/a0000197
D&A: Chapter 6
K: Chapter 2

Reduced models

Phase Space Analysis of Neuronal Excitability - J. Rinzel & B. Ermentrout, Methods in Neuronal Modeling (C. Koch and I. Segeve, Eds.)

One-dimensional neural systems

I: Chapter 3

Two-dimensional neural systems

I: Chapter 4

Subthreshold oscillations

HGR Talk 1
HGR Talk 2

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Suggested Papers for Student Projects

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Books

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).

Horacio
Last modified: Thu Sep 2 10:45:36 EDT 2010