Mathematical Models in Neuroscience

Jerry M. Wright wrightjm at erols.com
Tue Aug 20 05:46:22 EST 1996


BRUCE SHAPIRO <Bruce.E.Shapiro at jpl.nasa.gov> wrote:

>Has anyone out there taught - or taken - or know of - a graduate level 
>course in mathematical models in neuroscience (Besides the ones at 
>UCLA)?

>I will be co-teaching such a course this fall at UCLA and am looking 
>for suggestions/ideas/experience of those who have gone before.

>Topics include: concepts in modelling, modelling in-computo vs. 
>experiments in-vivo and in-vitro, Hodgkin-Huxley, Morris-Lecar, 
>Oscillation and Bursting, Neuronal Circuits, Cable Equations, etc.

>Bruce Shapiro
>Bruce.E.Shapiro at jpl.nasa.gov

I haven't taught a course but have given a couple of seminars on
selected topics.  These are some of the sources I used.



Methods in Neuronal Modeling: from sysnapses to networks
Koch and Segev eds
MIT Press, 1989, paper
ISBN 0-262-61071-X
The book is based upon a 4 week course in computational neurobiology
at the Marine Biological Laboratory in Woods Hole.

An introduction to the mathematics of neurons
Hoppensteadt
Cambridge University Press, 1986, paper
ISBN 0-521-31574-3
	Electrical circuits
	Neurons and some mathematical models
		Nernst, Hodgkin-Huxley, FitzHugh-Nagumo, VCON
	Clocks
	Phase locked loops
	Small networks
	Energy surfaces and stable firing patterns
		Hopfield’s model
	Synchronization in large networks

Introduction to theoretical neurobiology: 
Volume 1 Linear cable theory and dendritic structure
Volume 2 Nonlinear and stochastic theories
Tuckwell
Cambridge University Press, 1988, hard cover
ISBN 0-521-35096-4 (vol 1)
ISBN 0-521-35217-7 (vol 2)

Mathematical aspects of Hodgkin-Huxley neural theory
Cronin
Cambridge University Press, 1987, hard cover
ISBN 0-521-33482-9

Random Walks in Biology
Berg, H.C.
Princeton University Press, 1983, $12.99, paper
ISBN 0-691-00064-6
Models of diffusion:
	Microscopic theory
		1,2,3 dimensional random walks
		binomial and Gaussian distributions
	Macroscopic theory
		Fick’s equations, time-dependent and steady-state solutions
		Diffusion to N disk-like adsorbers on the surface of a sphere/planar
 			barrier [ion channels on a cell surface/lipid bilayer]
	diffusion to capture
	diffusion with drift
		electrophoresis, sedementation rate, Stoke’s law, 
	diffusion at equilibrium


Mathematics in medicine and the life sciences
Hoppensteadt and Peskin
Springer-Verlag, 1992, hard cover
ISBN 0-387-97639-6
Chapter 7 Control of cell volume and the electrical properties of cell
membranes
Chapter 10 Biological Clocks and Mechanisms of neural control

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