Special Topics: Modeling of Neuronal Dynamics
Course Number: MATH-GA 2863.001
Prerequisite: some familiarity with applied differential equations (seek consent of instructor if in
doubt).
Description: This course will focus on neurophysiology and biophysics at the cellular
level - the mechanistic and mathematical descriptions of neuronal dynamics and input/output
properties – some linear and many quite nonlinear. How do neurons integrate synaptic inputs
over their dendrites, generate spikes and transmit spikes to targets? With a range of different
intrinsic properties neurons can temporally organize their distinctive spiking signatures to
perform as integrators, as differentiators, as fast or slow pacemakers, or as bursters. Neuronal
functional architecture varies; different branching structures and ionic channel distributions
allow for local processing in dendrites or more feedforward transmission to the soma; coupling
between soma and axon can shape spike train output. Excitability and propagation will be
described with Hodgkin-Huxley-like models and reductions; synaptic transduction will feature
ionic channel kinetics, dynamics of depression/facilitation/plasticity and control at dendritic
spines. Both numerical simulation and analytical techniques (perturbation and bifurcation
methods) will be described and used, serving as an applied introduction to these methodologies.
Students will undertake computing projects related to the course material.