Introduction to Dynamical Models in Biology

Overview

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COURSE OUTLINE: Mathematical modeling has become an 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 the basics of analytical techniques, graphical techniques, and numerical simulation.

Syllabus

Mathematical modeling in biology.
How to Start Modeling.
Modeling the spread of infectious disease.
Modeling population growth.
Numerical solution of ODE 1.
Numerical solution of ODE 2.
Simulating ODE-based models:Introduction to JSim.
Simulating ODE-based models:Examples of simulation in JSim.
Steady state and stability analysis:Understanding Steady State.
Steady state and stability analysis:Stability of Steady States.
Phase Plane Analysis-I.
Phase Plane Analysis-II.
Concepts of Bifurcation: Introduction.
Concepts of Bifurcation: Bifurcation in Biological Systems.
Modeling Molecular Processes in Cell: Introduction.
Modeling Molecular Processes in Cell: Receptor-Ligand Interaction.
Modeling Molecular Processes in Cell:Enzymatic Processes.
Modeling Molecular Processes in Cell:Transcription and Translation.
Modeling Cell Signaling:Negative Feedback Motif.
Modeling Cell Signaling:Positive Feedback Motif.
Modeling Cell Signaling:Incoherent Feedforward Motif.
Modeling Transcriptional Circuits-1.
Modeling Transcriptional Circuits-2.
Online Resources for Mathematical Modeling in Biology.