Introduction to Computational Neuroscience

            Biol 635 / Math 635 / Biol432 / Math 430

            Fall 2021

    NJIT HONOR CODE:

    Academic Integrity is the cornerstone of higher education and is central to the ideals of this course and the university. Cheating is strictly prohibited and devalues the degree that you are working on. As a member of the NJIT community, it is your responsibility to protect your educational investment by knowing and following the academic code of integrity policy that is found at: Academic Honor Code - University Policy on Academic Integrity.

    Please note that it is my professional obligation and responsibility to report any academic misconduct to the Dean of Students Office. Any student found in violation of the code by cheating, plagiarizing or using any online software inappropriately will result in disciplinary action. This may include a failing grade of F, and/or suspension or dismissal from the university. If you have any questions about the code of Academic Integrity, please contact the Dean of Students Office at dos@njit.edu.

    Course Description:

    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, dynamical systems tools for the analysis of mechanisms of neural activity.

    Textbook:

      "An Introductory Course in Computational Neuroscience", by P. Miller - MIT PRess (2018), 1st edition, ISBN: 978-0260238256.

    Recommended Books:

      "Mathematical Foundations of Neuroscience", by G. B. Ermentrout & D. H. Terman - Springer (2010), 1st edition. ISBN 978-0-387-87707-5.

      "Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting", by Eugene M. Izhikevich. The MIT Press, 2007. ISBN 0-262-09043-8

      "Foundations of Cellular Neurophysiology", by Daniel Johnston and Samuel M.-S. Wu. The MIT Press, 1995. ISBN 0-262-10053-3.
      "Biophysics of Computation - Information processing in single neurons", by Christof Koch. Oxford University Press, 1999. ISBN 0-19-510491-9.

      "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

    Class meets:

      Tue: 6:00pm - 8:50pm

    Midterm project presenttions:

      TBA (in class)

    Office hours:

      TBA / By appointment (Also available in Webex, Zoom & Slack)

    Grading Policy:

      Biol635 & Math635 (Graduate):

      Homework, quizzes & class participation: .................. 40%

      Projects / Presentations: .............................................. 30%

      Midterm exam: ............................................................. 30%

      Biol432 & Math430 (Undergraduate):

      Homework, quizzes & class participation: .................. 40%

      Midterm exam: .............................................................. 30%

      Final Exam: .................................................................. 30%

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      Please note that the University Drop Date deadline will be strictly enforced

    Homework Policy

    Homework will consist of modeling and simulations exercises on the topics discussed in class. Homework assignments will be posted on this course website (see below).

      A number of assignments will be given out during the semester

      Assignments must be submitted on canvas

      Late homework will not be accepted

      The source code used in your calculations MUST accompany the submitted homework

      Upon request, students must be able to explain their results and codes

    Class Policies:

      Attendance and Participation: Students must attend all classes.

      Absences from class will inhibit your ability to fully participate in class discussions and problem solving sessions and, therefore, affect your grade

      Tardiness to class is very disruptive to the instructor and students and will not be tolerated

      Makeup Exam Policy: There will be no makeup exams, except in rare and extenuating situations where the student has a legitimate reason for missing an exam. The student must notify the NJIT Math office and the Instructor that he/she will miss an exam. In all cases, the student must present written verifiable proof of the reason for missing the exam, e.g., a doctor's note, police report, court notice, etc., clearly stating the date AND times of the mitigating problem.

      Cellular Phones: All cellular phones, beepers and other electronic devices must be switched off during class and exam times (except when specifically allowed by the instructor).

      Chatting in class using electronic devices will not be tolerated.

    Course Outline:


Week Topics of the Class Notes
1

Introduction to the course

Introduction to Computational Neuroscience and neural dynamics

Passive membrane properties - The passive membrane equation

LN-01

LN-02

LN-03

2

Ordinary differential equations (ODEs) - Review of analytical methods

Ordinary differential equations (ODEs) - Review of numerical methods

LN-04

Matlab Tutorial (KK)

ODE Templates (HGR)

3

Dynamics of the passive membrane equation LN-05
4

Integrate-and-fire models

The Hodgkin-Huxley model I

LN-06

LN-07

5

The Hodgkin-Huxley model II

The cable equation

LN-08
6

The cable equation II

Introduction to dynamical systems methods for neural models

Reduced one- and two-dimensional neural models

LN-09

7

One-dimensional neural models: Phase-space analysis I LN-10
8

Two-dimensional neural models: Phase-space analysis I LN-11
9

Two-dimensional neural models: Phase-space analysis II LN-11
10

Subthreshold oscillations: Two- and three-dimensional models

and

Subthreshold and suprathreshold resonance

11

Bursting: three-dimensional models LN-12
12

Synaptic Dynamics

Network Dynamics

LN-13

LN-14

LN-15

13

Project Presentations
14

Project Presentations
15

Project Presentations


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Department of Mathematical Sciences(DMS).

New Jersey Institute of Technology (NJIT).

Horacio
Last modified: Sun Oct 31 13:16:02 EDT 2010