Instructors: · Ivo F. Sbalzarini (IFS) · Axel Voigt (AV) · Andreas Deutsch (AD)
Synopsis:
This course teaches modeling and simulation techniques for spatially resolved dynamical systems in biology. You will learn to account for the geometry of a system and for transport in space. After repetition of the basics from mathematics and physics, you will model processes such as diffusion and flow, and simulate them in the computer using methods from numerical analysis.
The learning goal is the analysis of the dynamic behavior of biological systems with spatial structure. We will introduce the key concepts for formulating a model of the system behavior and performing computer simulation of the model using numerical methods.
Prerequisites:
from this minor program:
Discrete Algorithms for Computational Biology;
Statistical Principles and Computational Methods.
For students of Mathematics and Physics equivalent prerequisites are expected. This in particular includes basics of continuous mathematics and calculus (vector algebra, differential equations, calculus), as well as computer programming experience in any programming language.
For mathematics students, the prerequisites are the modules
Math-Ba-ANAA,
Math-Ba-ANAG,
Math-Ba-LAAG,
Math-Ba-MINT,
Math-Ba-NUM,
Math-Ba-NUME,
and Math-Ba-PROG.
Format:
4 SWS (2V+2U)
Exam
written (110 minutes)
Learning goals:
Modelling the dynamic behavior of biological systems with spatial structure
Formulation of a model of the system behaviour
Computer simulation of the model using numerical methods
Special remarks:
The course is part of the Computational Biology minor program.
Syllabus:
Lecture 1 : (IFS)
Introduction: when, where, and why modeling and simulation?
Lecture 2 : (IFS)
Modeling scaling: dimensional analysis
Lecture 3 : (IFS)
Modeling dynamics: the method of reservoirs and flows
Lecture 4 : (IFS)
Recap on Vector Analysis
Lecture 5 : (IFS)
Spatiotemporal modeling: control volume methods
Lecture 6 : (AV)
Examples and Applications: Diffusion
Lecture 7 : (AV)
Numerical simulation 1: the finite-difference method
Lecture 8 : (AV)
Numerical simulation 2: particle methods
Lecture 9 : (AV)
Examples and Applications: Advection-Diffusion
Lecture 10 : (AD)
Numerical simulation 3: discrete systems and CA
Lecture 11 : (AD)
Examples and Applications: collective cell behavior
Lecture 12 : (AD)
Examples and Applications: cancer invasion
Lecture 13 : (AD)
Examples and Applications: tissue regeneration