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

(Thoughts without content are empty, intuitions without concepts are blind.*)

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 such as propability and information theory, biophysics, and statistical mechanics are presented as needed.

There is no official textbook. Detailed lecture notes, with illustrations from relevant experimental papers, are provided as handouts, along with links to background material. There are four homework assignements plus a class project. For Winter 2025, we will have circuits constructed in neuromorphic hardware, with concurrent LTspice simulation as needed, as an option for the project. We build on the ideas of Prof. Marcello Rozenberg and use fed-back thyristors as spiking elements and current-mirrors as synapses to construct small neural circuits; see:

For Winter 2025, we are also pleased to have Mr. Haidong Qin as the class teaching assistant. Mr. Qin will run a tutorial and discussion section and hold office hours; office hours with Prof. Kleinfeld are immediately after class and by appointment.

Lecture notes for Winter 2024.

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

Tutorial and discussion sections

Homework (e-mail a type-set or scanned PDF to Ms. Ghita Guessous)

Historical lecture notes from Winter 2022.

Background material

*Immanuel Kant, 1724 - 1804, in Critique of Pure Reason.

**John von Neumann, 1903-1957.