Università Roma Tre

A summary treatment of the structure and function of the components of the nervous system on various scales is proposed, as well as an overview of the experimental techniques for measuring nervous activity.
In modeling in neuroscience it is not generally possible to clearly separate the scales of description of the problem, or simply import statistical mechanics techniques used for example in critical phenomena. We illustrate a series of approximations and simplifications that allow both a synthetic mathematical treatment of the single neuron, with the methods of the dynamical systems theory, and the construction of tractable models of networks of neurons.

Program

* Historical sketch
* Introduction to the structure of the central nervous system
* Neuron membrane and ionic channels
* Synaptic transmission
* Overview of experimental methods
* Ionic equilibrium and membrane potential
* Hodgkin-Huxley model of spike generation
* Features of dendrites
* Cable theory; elements of Rall's theory of dendritic trees
* Spike propagation
* 'Quasi-active' membrane; linearization of the Hodgkin-Huxley equations
* Bidimensional reduction of the Hodgkin-Huxley equations; phase plane analysis
* Elements of bifurcation theory and application to bidimensional neuron models
* Noise sources in neuronal dynamics
* Model of quantal release of neurotransmitters
* Stochastic dynamics of ionic channels
* General aspects of Poisson and renewal processes; application to the
description of spike trains
* ‘Integrate-and-fire’ (IF) neuron model with deterministic and stochastic
input
* Diffusion approximation for the IF neuron; Fokker-Planck equation
* Calculation of the mean firing rate in stationary regime; transfer function
* IF and ExpIF with spike frequency adaptation
* Elements of extensions of IF models
* Networks of IF neurons: mean field theory and attractors
* Excitation-inhibition balance
* Elements of synaptic plasticity and learning models
* Elements of Working Memory models
* Elements of perceptual decision models
* Elements of reservoir computing
* Elements of Deep Learning

Textbook: W. Gerstner, W.M. Kistler, R. Naud, L. Paninski, “Neuronal Dynamics”,
Cambridge University Press 2014
Chapter 1, Chapter 2, Chapter 3 (except 3.2.3), Chapter 4, Chapter 6 (6.1, 6.3.1),
Chapter 7 (till 7.5.3 included), Chapter 8, Chapter 12 (till 12.3.6 included,
12.4.1-12.4.4), Chapter 13 (till 13.4 included), Chapter 16 (16.1, 16.2), Chapter
17, Chapter 19 (19.1, 19.2), Chapter 20 (20.1).

The slides of the lectures will be distributed, with papers relevant to specific
aspects

Suggested references
B. Ermentrout, D. Terman, Mathematical foundations of neuroscience, Springer 2010
(Cap. 1, Cap. 6)
H. Tuckwell, Introduction to theoretical neurobiology, Cambridge University Press
1988 (Vol. 1 Cap. 4, Vol. 2 Cap.9)
D. Johnston, S. Wu, Foundations of cellular neurophysiology, MIT Press 1995 (Cap. 2,
Cap. 5, Cap. 9, Cap. 10)
S.H. Strogatz, Nonlinear dynamics and chaos, Perseus 1994 (Cap. 3, Cap. 6, Cap. 7,
Cap. 8)
D. Sterrat, B. Graham, A. Gillies, D. Willshaw, Principles of computational modeling
in neuroscience, Cambridge University Press 2011