Nonlinear Dynamics in Biological Systems

Click here to return to main Rickus Lab page

Coures Outline and Syllabus

This course is an introduction to nonlinear dynamics with applications to biology targeted to junior/senior engineering students and 1st year graduate students in engineering and quantitative life sciences.

Syllabus

Course Outline

We will use Strogatz as our main text and supplement with outside biological examples.

Organize Team Groups and Topics

Group 1: Dr. Rickus has a request that one group work on Bacterial Paper Rock Scissors. this is a project where 3 genetically engineered bacterial strains compete against each other in such away that 1 beats/kills 2, 2 beats/kills 3, and 3beats/kills 1. anyone game? Yes, group 'Grad Minority' is interested in taking on this project

Group 2 Circadian Rhyth. my name is ladida anyone wanna join

Group 4: A chemistry graduate student is looking for more people interested in intracellullar calcium oscillations (i.e. calcium induced calcium release). As of Friday after class, need 3-4 people. Contact mcgreen@purdue.edu

other possible ideas: microbial competion, metabolism, neuronal oscillations, cell cycle

neurological signals (3): Brandon Davis, Nicole Meehan, Omeed Paydar, Andrew Pierce

neuronal firing:(4) Timu Gallien, Julie Morby, Michelle Scheidt, Mark Wilson

cadiac modeling(5), Matt Croxall, Meghan Floyd, Erica Halsey, Shari Hatfield, Rohit Shah

bacterial rock paper scissors(3):Team Grad Minority. Alex DiMauro, Trisha Eustaquio, and Nick Snead

circadian rhythms(4): Jeremy Schaeffer, Arun Mohan , Drew Lengerich, Shaunak A Kothari

cell differentiation(4): Sarah Noble, Paul Critser, Prasad Siddavatam, Jiji Chen

team name: The Bowman Group, members: Chris Fancher, Todd Shuba, and Ben Zajeski and area of interest: Fermentation

Hospital sustainability(4): Steve Higbee, Halle Burton, Tyler MacBroom, Steven Lee

Team Name: The Metabolites, Members: Brooke Beier, Eric Brandner, Elizabeth Casey, Eric HodgmanAreas of interest: Metabolism and neuron cells, Potential Project Area: Metabolic flux of neuron cells during firing

Lecture Notes and Topics

Monday August 20 Lecture 1 powerpoint Wed Aug 22 in class covered: projects, email list, class wiki, state space, existence and uniqueness, trajectory, dimensionality, possible behavior of 1,2,3 D systems, coverting higher order and time dependent equations to state space, intro to stability, intro to vector fields, autocatalysis example Chapter 1 notes

Background Math to Brush Up On

these following things should be 2nd nature to you. if they are hazing from the summer fun, it would be best to brush up now.

1. sketching of common functions: exponentials [math]\displaystyle{ exp(ax) }[/math], [math]\displaystyle{ sin(x) }[/math], [math]\displaystyle{ cos(x) }[/math], [math]\displaystyle{ x / x+1 }[/math], more generally [math]\displaystyle{ ax^n /(x^n+b) }[/math], polynomials
2. taking derivatives of common functions
3. solving simple linear ODEs [math]\displaystyle{ dx/dt = kx }[/math]
4. finding eigenvalues and eigenvectors
5. Taylor series expansion
6. solving polynomials
7. complex numbers