Mathematica Tutorials

These tutorials were developed and used in teaching the research apprenticeship courses taught by the Center for Cell Dynamics. These tutorials are designed to rapidly familliarize students with Mathematica, dynamical systems theory, and building ordinary differential equation models of cytoplasmic processes and gene networks. These tutorials were designed to be used in sequence, but experienced Mathematica users may skip the first tutorial.

These tutorials require Mathematica 5.0 or higher to run. Mathematica is a commercial program developed by Wolfram Research, but many universities and research institutes have Mathematica site licenses; check with your computer department to see whether you can use a copy. Otherwise, you may view (but not execute) these tutorials by using the Wolfram Mathematica Player.

You are welcome to use these tutorials in your teaching, but must give credit to the original authors (see copyright notice in the Mathematica notebooks) and follow the rules of the GPL documentation license.

Links to Sim2D

1. Introduction to Mathematica: how to use some of Mathematica's basic functions, both as a graphing calculator and a math genius that can do all your calculus homework.
(Kerry Kim)


Links to Sim2D

2. Springs: Set up & solve the equations of motion for various simple spring systems (simple harmonic oscillation, dampened spring) and multi-spring systems. Preparation for mechanical models of the cytoskeleton in the next lab.
(Kerry Kim)


Links to Sim2D

3. Cytoskeleton: Modeling the cytoskeleton as a large system of springs. This will show you how to use Mathematica to generate a system of equations, and solve a simple 2-D model of an actively contracting cytoskeletal cortex.
(Kerry Kim)

Links to Sim2D

4. Enzyme Kinetics: Exploration of gene networks including reaction-diffusion (Turing models). Discussion of nullclines and phase plane analysis. You will also explore a hypothetical 2-gene cell cycle oscillator.
(Kerry Kim)


Links to Sim2D

5. Parameter searches: In this lab, you will write more powerful functions to systematically and randomly explore and visualize working parameter space for the networks in lab 4. (Kerry Kim)