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Michael Gray
A mathematical and computational introduction to the biophysical mechanisms that underlie physiological functions of single neurons and synapses. Topics include voltage-dependent channel gating mechanisms, the Hodgkin-Huxley model for membrane excitability, repetitive and burst firing, nerve impulse propagation in axons and dendrites, single- and multi-compartmental modeling, synaptic transmission, calcium handling dynamics and calcium dependent currents and processes.
Homework: ............ 30%
Midterm: ............... 30%
Project: ................. 30%
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Please note that the University Drop Date November 2, 2009 deadline will be strictly enforced
Class | Date | Topic of the Class | Lecture Notes |
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Aug 31
| General outline - Introduction to the Neurosciences |
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Sep 3
| Passive membrane properties |
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Sep 7
| Labor Day | . |
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Sep 10
| How to solve ODE's |
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Sep 14
| Introduction to XPP |
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Sep 17
| Dynamics of the passive membrane I |
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Sep 21
| Dynamics of the passive membrane II |
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Sep 24
| Integrate-and-fire neuron model |
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Sep 28
| The Hodgkin-Huxley model I |
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Oct 1
| The Hodgkin-Huxley model II |
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Oct 5
| The cable equation I |
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Oct 8
| The cable equation II |
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Oct 12
| Modeling and simulations issues | . |
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Oct 15
| Introduction to Dynamical Systems - Reduced neural models |
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Oct 19
| Reduced one- and two-dimensional neural models |
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Oct 22
| One-dimensional neural models: Phase-space analysis I |
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Oct 26
| One-dimensional neural models: Phase-space analysis II |
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Oct 29
| Review | . |
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Nov 2
| Exam | . |
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Nov 5
| Two-dimensional neural models: Phase-space analysis I |
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Nov 9
| Two-dimensional neural models: Phase-space analysis II |
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Nov 12
| Two-dimensional neural models: Phase-space analysis III |
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Nov 16
| Two-dimensional neural models: Phase-space analysis IV |
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Nov 19
| Subthreshold oscillations: Two- and three-dimensional models | . |
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Nov 20
| Subthreshold oscillations: The canard phenomenon | . |
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Nov 23
| Students Presentations: (1) Madhu, (2) Matthew | . |
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Nov 24
| Student Presentations (Tue): (3) Fatima, (4) Meera | . |
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Nov 27
| Thanksgiving Recess | . |
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Nov 30
| Student Presentations: (5) Temmy, (6) Nima, (7) Jay | . |
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Dec 3
| Student Presentations: (8) Bhaumik, (9) Juhyung, (10) Mohammed | . |
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Dec 7
| Student Presentations: (11) Yang, (12) Swathi, (13) Karina | . |
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| Final Exam Period | . |
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Department of Mathematical Sciences(DMS).
New Jersey Institute of Technology (NJIT).