Discrete Biological Models (2012/2013)

Course code
Name of lecturer
Giuditta Franco
Giuditta Franco
Number of ECTS credits allocated
Academic sector
Language of instruction
I semestre dal Oct 1, 2012 al Jan 31, 2013.

Lesson timetable

Learning outcomes

The course is designed to introduce several methodologies to model phenomena occurring in nature, by means of discrete mathematical tools and computational systems. The goal is to develop the ability of the student to master different approaches of discrete biological modeling, by means of the presentation of the state of the art and of the most recent problematics. Basic theoretical concepts (of mathematics, computer science, biology) are recalled, to better understand both traditional mathematical models and computational models of cellular and molecular processes, proposed along with a few case studies.


Part I (traditional mathematical models)
Introduction to different classes of models, namely to discrete models
Discrete mathematics fundamentals - induction and recurrence
Fibonacci numbers and golden section in nature
Growth dynamics of microorganisms and of bacterial cultures
Malthusian biological population growth (extended) models
Iterative biological models, recurrence equations solving criteria
Logistic map: stability analysis, periodic orbits, and chaotic behaviour
Lotka-Volterra prey-predator model
Cobweb model of supply/demand interaction
An example of probabilistic model: gambler's ruin

Part II (non-conventional bioinformatics models)
Formal languages and biological grammars
Computational models of bio-molecular processes
Computational complexity of bio-algorithms and NP-completeness
Informational structure of DNA molecule, operations, experimental techniques
Amplification processes for string recombination and concatenation
DNA algorithms solving SAT
Self-assembly biomolecular processes
Discrete models of metabolism
Biological networks
Algorithmic procedures based on bacterial growth, and related experimental techniques

Reference books
Author Title Publisher Year ISBN Note
Garey, M. R. and Johnson, D. S. Computers intractability: a guide to the theory of NP-completeness Freeman 1979 0-7167-1045-5
Gheorghe Paun, Grzegorz Rozenberg, Arto Salomaa DNA computing: new computing paradigms (Edizione 3) Springer 2013
David G. Luenberger Introduction to Dynamic Systems - Theory, Models, and Applications  
V. K. Balakrishnan Introductory Discrete Mathematics  

Assessment methods and criteria

Oral exam, or a couple of written midterm exams

Teaching aids