NMAK13001U Algebraic Methods in Biology (AlgBio)

Volume 2013/2014
Education
MSc Programme in Mathematics
Content
Algebraic and graph-based techniques to study interaction networks as dynamical systems modelled with differential equations. Interaction networks are structural representations of dynamical systems used in life sciences to study chemical, cellular or eco systems. The focus is on the so-called Chemical Reaction Network Theory, mainly an algebraic theory. The course comprises the mathematical foundations of the theory and classical results, the study of models with mass-action kinetics, number of steady states, characterization of  algebraic invariants, stability and oscillations. The course includes basic programming in Maple of the methods introduced in the class to study realistic biological systems. Knowing Maple beforehand is not required.
Learning Outcome
Knowledge: basics of chemical reaction network theory, what it is used for, what it can do and the advantages it has over numerical analysis and simulation; algebraic methods to determine if a network can have multiple steady states, algebraic methods to study stability properties of steady states and the existence of oscillatory behavior; the use of algebraic invariants to assess if a model fits given data; implement the methods using Maple; basic understanding of some biochemical processes.

Skills: by the end of the course the student will have acquired skills to prove small theorems in chemical reaction network theory; apply the methods to given examples; identify in what situations chemical reaction network theory can be of use and what techniques are suitable in a given casel;  reproduce, using algebraic techniques, conclusions of studies in the literature based on simulations.

Competences: by the end of the course the student will be able to rigorously analyze a model of an interaction network and answer mathematical questions that are relevant in biology; to design models with desired mathematical characteristics; to compare models and their properties; to criticize and discuss existing approaches in the literature.
General background in algebra, analysis, and differential equations, corresponding to that of a bachelor in mathematics
6h per week including lectures and exercises in a proportion of 3 to 3
  • Category
  • Hours
  • Exam
  • 45
  • Lectures
  • 21
  • Practical exercises
  • 21
  • Preparation
  • 105
  • Project work
  • 14
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Written assignment, 2 weeks
The evaluation is an individual two-week take-home exam consisting of a written project containing the detailed study of a biological system using the techniques learnt in the course (including programming). Systems will be taken from the literature and the study will include discussion of the mathematical approach in the original manuscript. Each student is assigned a different project.
Exam registration requirements
Two mandatory assignments by week 3 and 5 that have to be approved. If a mandatory assignment is not presented or approved, the student can present it again before the end of the course.
Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examiner
Re-exam
The two mandatory assignments (if not previously approved) and the final project.
Criteria for exam assesment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.