Mathematical Modelling and Scientific Computing in the Biosciences

Location: HF 9904
Time: Tuesdays 13:45-15:15
Lecturer: Dr. James Lu (Email: james.lu@oeaw.ac.at)

Course Overview

Biological Topics/Models

● Enzyme kinetics

        - Mass-action, Hill-Langmuir equation, Michaelis-Menton equation

● Neuron Dynamics

        - Hodgkin-Huxley model

● Cell Cycle

● Circadian Rhythm

Course Overview

Mathematical Topics

● Singular Perturbation

        - Applications to fast/slow time-scale separation, Hill-Langmuir equation

● Non-Dimensionalization

        - Buckingham Π-theorem

● Numerical ODE integration

        -Methods, accuracy, stability

● Dynamical Systems

        - Bifurcations: theory and numerics

● Inverse Problems

        - Parameter identification, inverse bifurcation and eigenvalue analyses

Course Overview

Computational Tools

● MathSBML

        - Mathematica package for reading and analysis of models encoded in the Systems Biology Markup-Language (SBML) format
        - Webpage: http://sbml.org/software/mathsbml/

● MATCONT

        - MATLAB package for bifurcation analysis of dynamical systems
        - Webpage: http://www.matcont.ugent.be/

● SBML ODE Solver Library

        - C library and command line application for numeric and symbolic analysis of SBML models
        - Webpage: http://www.tbi.univie.ac.at/~raim/odeSolver/

● SBML Inverse Eigenvalue Analyzer

        - Mathematica Add-On package for exploring possibility of qualitative dynamical behaviors via inverse eigenvalue analyis
        - Webpage: ongoing work, under development

Created by Mathematica  (March 4, 2007)