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. Aspects of applied mathematics, biophysics, and statistical mechanics are presented as needed.

There is no official textbook. Detailed lecture notes, with illustrations from relevant experimental papers, are provided below. 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 in 2702 Mayer Hall. For 2022, we are pleased to have Mr. Bin Wang as the class teaching assistant. Mr. Wang will run a tutorial and discussion section Thursday from 5:00 to 6:00 PM (2623 Mayer Hall or https://ucsd.zoom.us/j/93066192682). This will include homework review. Office hours with Mr. Wang are Tuesdays and Thursdays from Noon to 1:00 PM (133 CNCB or https://ucsd.zoom.us/j/93066192682) and with Prof. Kleinfeld (7108 Urey Hall) by appointment.

Lecture notes for Winter 2022.

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(Lecture 1) - Recurrent neuronal networks: A tale of two cells
DK lecture notes (5.4 MB PDF)
(Lecture 2) - Recurrent neuronal networks: Associative memory 1
DK lecture notes (2.0 MB PDF)
Statistical mechanics of neural networks - Sompolinsky reprint (4.0 MB PDF)
(Lecture 3) - Recurrent neuronal networks: Associative memory 2
DK lecture notes (3.8 MB PDF)
(Lecture 4) - Neurotechnology to measure and manipulate
DK lecture notes (14.8 MB PDF)
Electrophysiology in the age of light - Scanziani and Hausser reprint (2.2 MB PDF)
(Lecture 5) - Recurrent neuronal networks: Invariant 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 6) - Recurrent neuronal networks: Invariant 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 7) - Recurrent neuronal networks: Invariant tuning and continuous attractors 3
DK lecture notes (2.6MB PDF)
(Lecture 8) - Linear recurrent networks: Integration, line attractors and mono-stability
DK lecture notes (3.9 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 9) - Biophysics of conductance-based neuronal dynamics.
DK lecture notes (1.0 MB PDF)
Action potentials - Bean reprint (0.7 MB PDF)
(Lecture 10) - Voltage scales of neuronal dynamics.
DK lecture notes (3.0 MB PDF)
Channel motion - Berneche and Roux simulation (43.1 MB MOV)
(Lecture 11) - Recurrent neuronal networks: Derivation from conductance models
DK lecture notes (1.0 MB PDF)
(Lecture 12) - Variability in network dynamics. Part 1
DK lecture notes (3.9 Mb PDF)
van Vreeswijk & Sompolinsky reprint (0.8 MB PDF)
Barral & Reyes reprint (1.7 MB PDF)
(Lecture 13) - Variability in network dynamics. Part 2
DK lecture notes (3.3 MB PDF)
Sanzeni, Akitake, Goldbach, Leedy, Brunel & Histed reprint (2.7 MB PDF)
(Lecture 14) - Spike dynamics in brutalized conductance models
DK lecture notes (4.2 MBb PDF)
Dimensional reduction - Rinzel reprint (1.8 MB PDF)

The Beach Boys in 1966

(Lecture 15) - Coupled oscillators and waves in the brain. Part 1
DK lecture notes (1.0 MB PDF)
Coupled oscillators - Ermentrout & Kleinfeld reprint (0.6 MB PDF)
(Lecture 16) - Coupled oscillators and waves in the brain. Part 2
DK lecture notes (3.7 MB PDF)
(Lecture 17) - Coupled oscillators and waves in the brain. Part 3
DK lecture notes (9.5 MB PDF)
(Lecture 18) - Synaptic weights from space-time receptive fields
DK lecture notes (3.9 MB PDF)
(Lecture 19) - Layered networks for optimal stimulus reconstruction
DK lecture notes (0.3 MB PDF)
Simplified neuron model as a principal component analyzer - Oja reprint (0.3 MB PDF)

Darly Hannah and Rutger Hauer in Blade Runner

Homework (e-mail a type set or scanned PDF to Mr. Bin Wang)

Number 1: Due midnight on 24 Jan (0.2 MB ZIP)
Number 2: Due midnight on 11 Feb (3.8 MB ZIP)
Number 3: Due midnight on 28 Feb (0.2 MB ZIP)
Number 4: Due midnight on XX Mar (X.X MB PDF)
Suggested manuscripts for projects. Presentations are on Thursday 17 Mar; hardcopy due midnight on Friday 25 Mar (91.3 MB ZIP)

Tutorial and discussion sections (updated as needed)

13 Jan - Review of linear algebra
20 Jan - Review of Fourier transform / HW
27 Jan - Review of ordinary differential equations
3 Feb - Review of conductance based equations / HW
10 Feb - Review of Poisson variability
17 Feb - Project Discussions
24 Feb - Review of dynamics and stability / HW
3 March - Review of front propagation / HW
10 March - HW and Project Review

Background material

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)