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 described by the phase in its limit cycle. 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 its Poisson firing rate. 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 offical textbook for the class, although much 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 2623 Mayer Hall. Lectures are every Tuesday and Thursday from 8:00 to 9:20 AM. Ms. Mendy Hsu, the class teaching assistant, will run a discussion section from 6:00 to 7:00 PM every Wednesday. This will include pedagogical material and homework review. Office hours with Ms. Hsu are 9:30 to 10:30 AM in room 2218 Mayer Hall on both Tuesday sand Thursdays (directly after class) and by appointment.

Preliminary lecture schedule, notes, and source material for Winter 2019

(Week 1) 8, 10 Jan - Basic neuronal anatomy, electrical dynamics, and computation
DK lecture notes (0.2 Mb PDF)
DK lecture graphics (76.1 Mb PDF)
Connectomics - Kasthuri et al. reprint (5.3 Mb PDF)
(Week 2) 15, 17 Jan - Biophysical basis of action potentials: Insight through reduced neuronal dynamics
DK lecture notes on Hodgkin-Huxley model (0.2 Mb PDF)
DK lecture notes on reduced spike model (0.2 Mb PDF)
DK lecture graphics (15.8 Mb PDF)
Dimensional reduction - Rinzel reprint (1.8 Mb PDF)
Action potentials - Bean reprint (0.7 Mb PDF)
(Week 3) 22, 24 Jan - Cortical noise 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 4) 29 Jan (1 Feb - no class; 13 Feb make-up ) - Networks of neuronal oscillators and coupled phase dynamics
DK lecture notes on phase dynamics (0.2 Mb PDF)
DK lecture graphics (26.0 Mb PDF)
Coupled oscillators - Ermentrout & Kleinfeld reprint (0.9 Mb PDF)
(Week 5) 5, 7 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 (5.8 Mb PDF)
Line attractors - Seung reprint (0.5 Mb PDF)
Integrator networks - Major & Tank reprint (1.1 Mb PDF)
(Week 6) 12, 14 Feb - Nonlinear recurrent networks: Basis for associative memory and application to motor programs
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 7) 19, 21 Feb - Nonlinear recurrent networks: Derivation of rate equations from conductance models.

Discussion of group projects
DK lecture notes on derivation of rate-based networks (0.3 Mb PDF)
DK lecture graphics (0.1 Mb PDF)
Gain curves - Chance, Abbott & Reyes reprint (0.2 Mb PDF)
(Week 8) 26, 28 Feb - Nonlinear recurrent networks: Invariant tuning and stable "bumps" of network activity
DK lecture notes on the ring attractor (0.1 Mb PDF)
DK lecture graphics (3.0 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)
Integrator networks - Seelig & Jayaraman reprint (5.7 Mb PDF)
(Week 9) 5 Mar (7 Mar - no class) - Feed forward computation with Perceptrons and multi-layered networks
DK lecture notes on layered networks (0.3 Mb PDF)
DK lecture graphics (9.7 Mb PDF)
MATLAB code for Perceptron learning from Seung (0.1 Mb M)
MATLAB Data (3.3 Mb Mat)
Vision and gaze - Zipser & Andersen reprint (0.8 Mb PDF)
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)
Vision-based identification - Abbasi-Asla, Chenb, Bloniarzb, Oliverc, Willmorec, Gallant & Yu reprint (4.0 Mb PDF)
(Week 10) 12, 14 Mar - Subcellular dynamcs and the tools for subcellular measurements
DK lecture notes and graphics on dendritic attenuation and gain (3.0 Mb PDF)
Dendrites - London & Häusser reprint (0.8 Mb PDF)
Dendrites - Magee reprint (0.9 Mb PDF)
Dendrites - Polsky, Mel & Schiller reprint (1.3 Mb PDF)
Functional measurements - Scanziani & Häusser reprint (2.1 Mb PDF)

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

Number 1: Due midnight on 27 Jan (0.5 Mb ZIP)
Number 2: Due midnight on 10 Feb (2.7 Mb ZIP)
Number 3: Due midnight on 24 Feb (0.4 Mb ZIP)
Number 4: Due midnight on 17 Mar (0.3 Mb PDF)
Potential group project: Presentations are on 21 Mar (3.2 Mb PDF)

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 dimensiona 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 of 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)