Physics 178/278 - The biophysical basis of neurons and networks

(Truth is much too complicated to allow anything but approximations.*)

Course overview

This course explores underlying principles and design rules for the neuronal circuits that control animal behavior. The emphasis in on analytically tractable models of neuronal network dynamics and computation. We present analytical pathways that involve dimensionality reduction to go from the "exact" dynamics of single neurons and synapses to simplified but tractable aspects of network activity. One case involves networks of coupled neurons with arhythmic firing rates that form extensive recurrent connections. Here, the interactions among neurons are strong and can lead to attractor dynamics. Such circuits serve to understand motor control, sensory processing, and memory.A second case involves networks of coupled neuronal oscillators in which each neuron is rhythmically active and described by its phase in a limit cycle. Here, the interactions among neurons affect only the relative timing between neurons. These networks provide a means to understand behaviors that range from locomotion to neurovascular dynamics in fMRI. A special aspect of the class is the inclusion of ongoing efforts in connectomics to bridge prediction and experimental reality. Subtopics, aspects of applied mathematics, and experimental techniques are discussed as needed.

There is no official textbook. Detailed lecture notes are provided along with accompanying graphics from relevant experimental papers. A fraction of the underlying mathematics is covered in "Foundations of Mathematical Neuroscience" by Bard Ermentrout and David Therman (9.2 MB PDF).

The class meets online in Winter 2021. "Zoom" lectures (https://ucsd.zoom.us/j/4601032208) are every Tuesday and Thursday from 8:00 to 9:20 AM PST. Mr. Lawson Fuller and Mr. Huanqiu Zhang, the class teaching assistants, will run tutorial and discussion sections every Monday from 4:00 to 5:00 PM and everyThursday from 4:00 to 5:00 PM; Zoom address to be provided. This will include pedagogical material and homework review. Office hours with Mr. Fuller and Mr. Zhang are immediately after class (Tuesdays and Thursdays from 9:30 to 10:30 AM PST) and with Prof. Kleinfeld by appointment; Zoom addresses to be provided.

Lecture notes for Winter 2021 will be posted just prior to class followed by corrected / updated versions.

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(Lecture 1) 5 Jan - Recurrent neuronal networks: A tale of two cells
DK lecture notes (4.2 MB PDF)
(Lecture 2) 7 Jan - Recurrent neuronal networks: Associative memory 1
DK lecture notes (2.3 MB PDF)
Statistical mechanics of neural networks - Sompolinsky reprint (4.0 MB PDF)
(Lecture 3) 12 Jan - Recurrent neuronal networks: Associative memory 2
DK lecture notes (1.0 MBb PDF)
(Lecture 4) 14 Jan - Recurrent neuronal networks: Invaraint tuning and continuous attractors 1
DK lecture notes (4.6 MB PDF)
Invariant tuning - Shapley & Sompolinsky reprint (1.1 MB PDF)

Attractor dynamics in the fly brain - Kim, Rouault, Druckmann & Jayaraman reprint

(5.3 MB PDF)
(Lecture 5) 19 Jan - Recurrent neuronal networks: Invaraint tuning and continuous attractors 2
DK lecture notes (0.5 MB PDF)
Modeling feature selectivity in local cortical circuits - Hansel & Sompolinsky book chapter reprint (3.7 Mb PDF)
(Lecture 6) 21 Jan - Recurrent neuronal networks: Invaraint tuning and continuous attractors 3
DK lecture notes (2.0MB PDF)
NeuroPhotonics review material (12.3 MB PDF)
(Lecture 7) 26 Jan - Linear recurrent networks: Integration, line attractors and mono-stability
DK lecture notes (3.5 MB PDF)
Juvenile zebrafish swimming - from Ahrens (5.2 MB MOV)
Juvenile zebrafish "fictive" swimming - from Ahrens (8.3 MB MOV)
Line attractors - Seung reprint (0.5 MB PDF)
Integrator networks - Major & Tank reprint (1.1 MB PDF)
(Lecture 8) 28 Jan - Biophysics of conductance-based neuronal dynamics. Part 1
DK lecture notes (1.8 MB PDF)
Action potentials - Bean reprint (0.7 MB PDF)
(Lecture 9) 2 Feb - Biophysics of conductance-based neuronal dynamics. Part 2
DK lecture notes (0.5 MB PDF)
Channel motion - Berneche and Roux simulation (43.1 MB MOV)
(Lecture 10) 4 Feb - Recurrent neuronal networks: Derivation from conductance models
DK lecture notes (1.0 MB PDF)
(Lecture 11) 9 Feb - Spike dynamics in brutalized conductance models
DK lecture notes (4.2 MBb PDF)
Dimensional reduction - Rinzel reprint (1.8 MB PDF)
11 Feb - Catch-up and project discussion
DK project notes (0.3 MB PDF)
(Lecture 12) 16 Feb - Coupled oscillations and waves in the brain
A graphic survey of oscillations and waves in the brain (23.5 MB PDF)
Coupled oscillators - Ermentrout & Kleinfeld reprint (0.6 MB PDF)
(Lecture 13) 18 Feb - Pairs and networks of neuronal oscillators. Part 1
DK lecture notes (0.6 MB PDF)
(Lecture 14) 23 Feb - Pairs and networks of neuronal oscillators. Part 2
DK lecture notes (0.3 MB PDF)
(Lecture 15) 25 Feb - Variability in neuronal eletrical dynamics.
DK lecture notes on thermal noise (0.3 MB PDF)
A graphic survey of intracellular and synaptic noise (2.0 MB PDF)
(Lecture 16) 2 Mar - Variability in neurons and networks. Part 1
DK lecture notes (2.1 Mb PDF)
van Vreeswijk & Sompolinsky reprint (0.8 MB PDF)
Barral and Reyes reprint (1.7 MB PDF)
(Lecture 17) 4 Mar - Variability in neurons and networks. Part 2
DK preliminary lecture notes (0.5 MB PDF)
(Lecture 18) 9 Mar - Synaptic weights from receptive fields and stimulus reconstruction
DK lecture notes (3.3 MB PDF)
(Lecture 19) 11 Mar - Layered networks
DK lecture notes (2.7 MB PDF)

Darly Hannah and Rutger Hauer in Blade Runner

Homework (e-mail a type set or scanned PDF to Mr. Lawson Fuller)

Number 1: Due midnight on 24 Jan (0.3 MB ZIP)
Number 2: Due midnight on 15 Feb (3.4 MB ZIP)
Number 3: Due midnight on 22 Feb (0.6 MB ZIP)
Number 4: Due midnight on 12Mar (0.4 MB PDF)
Group project presentations are on 18 Mar; hardcopy due midnight on 26 Mar (0.3 MB PDF)

Tutorial and discussion sections (updated as needed)

11 Jan - Introduction to MatLab
14 Jan - Linear Algebra I
18 Jan - Linear Algebra II
21 Jan - Homework Review I
25 Jan - Fourier Series
28 Jan - Poisson Variables
01 Feb - Ordinary Differential Equations
04 Feb - Homework Review II
11 Feb - Cable equation
18 Feb - Homework Review III
04 Mar - Homework Review IV

Background material

"Neuroscience: Exploring the Brain" by Mark Bear, Barry Connors and Michael Paradiso (49.6 MB PDF)
Review of diffusion. Notes and graphics of DK (0.3 MB PDF)
Review of electrodiffusion across membranes. Notes and graphics of DK (3.8 Mb PDF)
Review of electrotonic properties of dendrites and axons. Notes and graphics of DK. (0.7 MB PDF)
Review of Hodgkin Huxley formalism: Chapter 6 from "Biophysics of Computation" by Christoff Koch. (28.0 MB PDF)
Review of mammalian CNS anatomy. MBL Neuroinformatics graphics of Helen Basbas. (1.7 MB PDF)
Review of linear algebra. MBL Neuroinformatics notes of DK. (2.1 MB PDF)
Stability analysis of a two dimensional dynamical system. Notes of Yonitan Aljadeff. (0.1 MB PDF)
Review of Fourier transforms. Notes of DK. (0.1 MB PDF)
Review of Poisson distribution. Notes of John Cooper. (0.1 MB PDF)
Review of neuronal variability and Poisson statistics. Notes of Yonitan Aljadef. (0.1 MB PDF)
Receptive fields and predicting stimuli from spike trains. Notes of DK. (5.7 MB PDF)
Review of layered networks - Chapter 6 from "Neural Networks: A Comprehensive Foundation" by Simon Haykin. (11.5 MB PDF)
Reverse correlation, stimulus design, and analysis. Notes of Yonitan Aljadeff. (7.7 MB PDF)
"Analysis of spike trains" - Aljadeff, Lansdell, Fairhall & Kleinfeld reprint. (7.8 MB PDF)
"Spectral methods" - Kleinfeld & Mitra reprint. (5.3 MB PDF)
Basic MATLAB tutorial: Notes of Douglas Rubino. (0.1 MB M-code)
Advanced Matlab tutorial. (0.1 Mb zipped M-code)

*John von Neumann (1903-1957)