Introduction to Dynamical Models in Biology


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Mathematical modeling has become integral part of different fields of biology, from ecology to cell biology. This course is intended to introduce students of biology to elementary mathematical concepts and tools for dynamical models. The course will focus on modeling using ordinary differential equations (ODEs). We will start with basic mathematical concepts of ODE-based models and then connect those with experimental biology. Mathematical models will be on cellular and molecular processes in biology, like cell signaling, and transcriptional networks. Students will learn basics of analytical techniques, graphical techniques, and numerical simulation. 


Week 1:
Lecture 1: Introduction to mathematical modeling in biology
Lecture 2: How to start modeling?
Lecture 3 & 4: Basic concepts of modeling using ordinary differential equations
Lecture 5 & 6: Numerical solution of ODE-based models 

Week 2
Lecture 1 & 2: Simulating ODE-based models
Lecture 3 & 4: Steady state and stability analysis
Lecture 5 & 6: Phase plane analysis

Week 3:
Lecture 1 & 2: Concepts of bifurcation
Lecture 3 - 6: Mathematical formulations for elementary molecular processes

Week 4
Lecture 1 & 2: Modeling cell signaling
Lecture 3: Properties of feedback and feed-forward network motifs
Lecture 4 & 5: Modeling transcriptional circuits
Lecture 6: Online resources for mathematical modeling in biology