Can you provide me the course structure for PS 762: Introduction to Computational Neuroscience under Pre-Ph d Courses in Physical Sciences offered by JNU (Jawaharlal Nehru University)?

The course structure for PS 762: Introduction to Computational Neuroscience under Pre-Ph d Courses in Physical Sciences offered by JNU (Jawaharlal Nehru University) is as follows:

PS 762: Introduction to Computational Neuroscience

A major effort is currently under way to understand the operation of the central nervous system, and more specifically, of neuronal networks in the brain. This is of great importance at not only the theoretical level, but also for the possibility of understanding the causes and cures for diseases such as Alzheimer’s and Parkinson’s.

The approach presently being taken includes both experimental studies and theoretical and computational modeling to jointly address questions that arise in this area of research. There is an increasing need for scientists trained at the interface of these disciplines who possess a strong analytic background together with a solid understanding of biological phenomena.

The present course will teach students the basic set of mathematical and computational techniques required for them to pursue higher level research in the field of neuroscience. It would also prepare them, in part, to be able to move on to various industry jobs that require quantitative and analytic skills. For example, several pharmaceutical companies are actively seeking employees with the background to model and simulate processes on the computer prior to production and testing. The set of lectures will cover necessary techniques to be able to understand various biological questions, to address them mathematically and computationally and then to translate results into a language that is accessible to experimentalists. It is envisioned that students who pass this class will be able to immediately utilize their course work in either an experimental lab or on the way towards a PhD. Further the mathematical content of the course is sufficiently general that it will also allow students to work in modeling of biological problems outside of neuroscience, in fields such as genomics, protein signaling networks and even ecology.

This Pre-Ph.D. course will be accessible to final year students of the M.Sc.(Physics) program as well as those of the M.Sc.(Life Sciences) and that it could be an optional course in the M Tech. (Systems Biology) programme as well.

Pre-requisites: Calculus of many variables, a basic understanding of differential equations, ability to use computer software such as MATLAB and the ability to code in Fortran, C, C++ etc.

Course Outline [Approximate number of lectures per topic]

Introduction to neuroscience with description of some specific neuronal systems [2]

Mathematical background – Introduction to dynamical Systems, review of basics of differential equations, introduction to phase plane analysis, dimensional reduction techniques including timescale separation ideas [5]

Computational techniques – Introduction to relevant computer software such as XPP and Matlab Classes during this time to be held in a computer lab in a tutorial manner with demonstrations of software usage [5]

Models of single neurons – Derivation of the Hodgkin-Huxely equations and various reductions such as the FitzHugh-Nagumo and Morris-Lecar models Analysis of these and other basic models such as the Integrate and Fire model [6]

Models of synaptic interactions – Description of synapses and neurotransmitter release. Mathematical models for excitatory and inhibitory synapses. Models for short-term synaptic plasticity [6]

Small network dynamics – Focus on understanding and characterizing the dynamics of small networks of excitatory, inhibitory or mixed-type neurons. Detailed analysis of conditions leading to complete synchronization, phase locking or chaotic behavior in such networks [8]

Case studies –The dynamics of several specific biological examples will be explored including problems from the following areas: place cells in the hippocampus, sleep rhythms and oscillations of the thalamus, irregular activity in the basal ganglia, working memory models of the cortex and phase lag models of central pattern generators. [8]

Textbooks:
The following are list of suggested textbooks, although the course will initially be taught from a set of lecture notes.
1. 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
2. Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting, by Eugene M. Izhikevich. The MIT Press, 2007 ISBN 0-262-09043-8
3. Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students, by Bard Ermentrout, SIAM 2002 ISBN 0-89871-506-7