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 the cellular and synaptic basis for neuronal control of animal behavior. The emphasis in on analytically tractable models of network dynamics and neuronal computation. We provide a path from the dynamics of single neurons to three forms of network activity, each of which involves models where the description of a neuron is reduced to a single state-variable. The first involves networks of weakly coupled neuronal oscillators in which each neuron is rhythmically active and described by a firing rate and the phase in its limit cycle, while the interactions depend only on phase differences. These networks provide a natural means to discuss collective dynamics, such as oscillations and waves in networks of inhibitory neurons. The second and third forms of activity involve circuits of asynchronous neurons in which each cell is described by a Poisson firing rate and synaptic currents. Recurrent architectures provide a natural means to discuss attractor-based circuits for motor control, sensory processing and memory. Feedfoward architectures provide a means to formalize the logic of both single cells with large dendritic fields and motivate the concept of receptive fields. Both architectures provide design rules to determine connections in terms of the desired output state(s). Aspects of applied mathematics and experimental procedures are discussed as needed.

There is no official textbook for the class, although detailed lecture notes are provided for all of the relevant derivations, along with accompanying graphics from relevant experimental papers. A fraction of the underlying mathematics is covered in the excellent textbook "Foundations of Mathematical Neuroscience" by Bard Ermentrout and David Therman (9.2 Mb PDF).

The class meets in room 2702 Mayer Hall in Winter 2020. Lectures are every Tuesday and Thursday from 8:00 to 9:20 AM. Ms. Mendy Hsu and Mr. Huanqiu Zhang, the class teaching assistants, will run a discussion section from 6:00 to 7:20 PM every Tuesday on 2702 Mayer Hall. This will include pedagogical material and homework review. Office hours with Ms. Hsu and Mr. Zhang are 9:30 to 10:30 AM in room 2218 Mayer Hall (enter from plaza) on both Tuesday sand Thursdays and by appointment. Mr. Pantong Yao will further assist with the preparation of homework and class notes.

Lecture schedule, notes, and source material for Winter 2020

(Week 1) 7, 9 Jan - Basic neuronal anatomy, electrical dynamics, and computation
DK lecture notes on voltages and noise (0.2 Mb PDF)
DK lecture graphics (97.4 Mb PDF)
Connectomics - Kasthuri ... Lichtman reprint (5.3 Mb PDF)
Connectomics - Motta ... Helmstaedter reprint (5.7 Mb PDF)
(Week 2) 14, 16 Jan - Electrochemistry and biophysical basis of action potentials
DK lecture notes on Hodgkin-Huxley model (0.2 Mb PDF)
DK lecture graphics (14.6 Mb PDF)
Dimensional reduction - Rinzel reprint (1.8 Mb PDF)
Action potentials - Bean reprint (0.7 Mb PDF)
(Week 3) 21, 23 Jan - Reduced spiking models: Insights and transition to phase coupled dynamics
DK lecture notes on reduced spike model (0.2 Mb PDF)
DK lecture notes on phase dynamics (0.4 Mb PDF)
DK lecture graphics (23.1 Mb PDF)
Dimensional reduction - Rinzel reprint (1.8 Mb PDF)
(Week 4) 28 Jan - Networks of neuronal oscillators (30 Jan - Mr. Huanqiu Zhang linear algebra review)
DK lecture notes on phase dynamics (0.4 Mb PDF)
DK lecture graphics (5.1 Mb PDF)
Coupled oscillators - Ermentrout & Kleinfeld reprint (0.9 Mb PDF)
(Week 5) 4, 6 Feb - Linear recurrent networks: Basis of integration in motor control (line attractors)
DK lecture notes on linear networks (0.1 Mb PDF)
DK lecture graphics (14.7 Mb PDF)
Line attractors - Seung reprint (0.5 Mb PDF)
Integrator networks - Major & Tank reprint (1.1 Mb PDF)
(Week 6) 11, 13 Feb - Derivation of rate equations from conductance model - Discussion of group projects.
DK lecture notes on derivation of rate-based networks (0.3 Mb PDF)
DK lecture graphics (8.8 Mb PDF)
Gain curves - Chance, Abbott & Reyes reprint (0.2 Mb PDF)
(Week 7) 18, 20 Feb - Nonlinear recurrent networks: Invariant tuning and stable "bumps" of network activity
DK lecture notes on the ring attractor model (0.3 Mb PDF)
DK lecture graphics (3.8 Mb PDF)
Invariant tuning - Shapley & Sompolinsky reprint (1.1 Mb PDF)
Modeling feature selectivity in local cortical circuits - Hansel & Sompolinsky book chapter reprint (3.7 Mb PDF)
Heading networks - Seelig & Jayaraman reprint (5.7 Mb PDF)
(Week 8) 25, 27 Feb - Nonlinear recurrent networks: Application to associative memory
DK lecture notes on associative networks (0.2 Mb PDF)
DK lecture graphics (2.0 Mb PDF)
Statistical mechanics of neural networks - Sompolinsky reprint (4.0 Mb PDF)
Central pattern generators - Kleinfeld & Sompolinsky reprint (1.5 Mb PDF)
(Week 9) 3, 5 Mar - Fluctuations in neuronal output and "balanced" networks
DK lecture notes on noise and balanced networks near equilibrium (0.1 Mb PDF)
DK lecture graphics (6.6 Mb PDF)
van Vreeswijk & Sompolinsky reprint (0.8 Mb PDF)
Barral and Reyes reprint (1.7 Mb PDF)
(Week 10) 10, 12 Mar - Computation with Perceptrons / Active dendrites
DK lecture notes on layered networks (0.3 Mb PDF)
DK lecture graphics on layered networks (9.7 Mb PDF)
MATLAB code for Perceptron learning from Seung (0.1 Mb M)
MATLAB Data (3.3 Mb Mat)
Vision-based identification - Serre, Oliva & Poggio reprint (0.9 Mb PDF)
Vision-based identification - Yamins, Hong, Cadieu, Solomon, Seibert & DeCarlo reprint (1.8 Mb PDF)
DK lecture notes on dendritic gain (0.1 Mb PDF)
DK lecture graphics on dendritic gain (2.8 Mb PDF)

Darly Hannah and Rutger Hauer in Blade Runner

Homework (e-mail a type set or scanned PDF to Ms. Mendy Hsu)

Number 1: Due midnight on 26 Jan (2.8 Mb ZIP)
Number 2: Due midnight on 11 Feb (0.4 Mb)
Number 3: Due midnight on 01 Mar (0.3 Mb ZIP)
Number 4: Due midnight on 15 Mar (0.3 Mb PDF)
Group project presentations are on 19 Mar; hardcopy due 26 Mar (2.5 Mb PDF)

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)