Neuron Modeling Tutorial

This is a single neuron modeling tutorial developed for the Imbizo 2023 Summer School.

Note: This tutorial was edited for the Imbizo 2025 Summer School.

Title: Neuron Modeling and Ordinary Differential Equations

Key Learning Objectives:

• The tutorial's aim is to develop a deep intuition for single neuron modeling, and it is in 2 parts*.
• First is to build a mathematical intuition of first order ordinary differential equations (ODEs), practice analytical and numerical solutions of ODEs, and apply this mathematical knowledge to understand logistic functions as a building block for neuron models.
• Second is to use knowledge of logistic functions to understand leaky integrate and fire (LIF) neuron models and interrogate the model's input-output relationship by exploring input noise, spike frequency, and spike regularity.
• *Extended Homework encourages students to try implementing nonlinear Integrate and Fire (IF) neuron models and conductance-based neuron models using the material covered in the tutorial

Basic/Foundational Math concepts:

• Calculus - derivation and integration examples are solved by stepping through the steps of integration as a review for students
• Differential Equations ODE tutorial is for students without this math background

Tutorial Outline:

• Ordinary Differential Equations Tutorial
  • What is a Differential Equation?
  • Methods of Solution: Analytic and Numerical
  • Constant Growth (Linear Model)
  • Proportional Growth/Decay (Exponential Model)
  • Growth as an asymptote (Logistic Model)
• Leaky-Integrate-and-Fire Tutorial
  • A Return to the Hodgkin Huxley (HH) Equations
  • Building a LIF Model
  • Describing an LIF Model's Input/Output Relationship
    • Visualize LIF Voltage Trace with input noise
    • Generate an Frequency-Current (F-I) Curve
      • How does input noise impact the F-I curve of a LIF Model?
    • Measuring and Visualizing Inter-Spike-Intervals
      • Given a current input, how regularly or irregularly does a neuron spike?
    • Coefficient of Variance
• *Extended Homework
  • More practice with solving ODEs
  • Implementing and Analyzing the Input/Output Relationships of Nonlinear IF Models and IF Models with Adaptation
  • Implementing and Analyzing the Input/Output Relationships of the Hodgkin-Huxley Model

Access the Tutorials Below

• Tutorial 1: ODEs (solutions)

• Tutorial 2: Leaky Integrate and Fire Models (solutions)

If running offline, clone the repositories and find the notebooks in the "notebooks" directory.

• Tutorial 1: notebooks/Offline_01_ode_tutorial.ipynb
• Tutorial 2: notebooks/Offline_02_lif_tutorial.ipynb