Physics 178/278 - Biophysics and dynamics 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.

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

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 focus on two types of projects.

One set of projects focuses on associative networks in honor of this year's Nobel Prize in Physics to Prof. John Hopfield. We will consider theoretical papers that extend the original work and experimental papers that claim to provide evidence for line and ring attractors, as well as bistable and multistable point attractors.

A second set of projects 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 in hardware. Laboratory space and electronic gear for these projects is set aside in 7130 Urey Hall.

Photograph: Mr. Sincheng Huang demonstrates spiking of a thyistor-neuron (blue trace) after accumulation of synaptic inputs (yellow trace) from a current source (green trace).

For Winter 2025, we are pleased to have Mr. Haidong Qin as the class teaching assistant. Mr. Qin will help run an optional discussion section every Friday at 8:00 - 8:50 AM in Mayer 5301 and will hold an office hour immediately after class. Office hours with Prof. Kleinfeld are immediately after class and by appointment.

Lecture notes for Winter 2025

("Chapters" comprise one to three 1-1/3 hour lectures).

Optional discussion sections

Homework (upload through the Gradescope for this class using Entry Code:6J26X6)

Bonus lectures on neuronal biophysics

Suggested publications for 2025 literature deconstruction project

Literature for thyristor-neuron project

Background material

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

**John von Neumann, 1903-1957.