https://studiegids.vu.nl/en/courses/2026-2027/X_418154This course focuses on teaching the creation and analysis of mathematical models for biological systems across various levels of organization, from molecular circuits to cellular systems and potentially ecosystems. The primary modelling formalism explored is ordinary differential equations (ODEs), providing a foundation for understanding biological dynamics. The course aims to equip students with the ability to reproduce models from scientific literature and apply them to solve practical problems. It combines lectures with workgroups involving problem-solving using both computational tools (Python) and pen and paper. Learning Goals:Learn to develop and analyse mathematical models (primarily ODE-based) for diverse biological networks (molecular, cellular, etc.).Understand how to represent biological processes, particularly molecular mechanisms like enzyme kinetics and protein regulation, using mathematical formalisms like state-transition diagrams and mass-action kinetics.Gain proficiency in simplifying complex mechanisms into net process models suitable for integration into larger system models.Develop the skills to reproduce existing models from scientific papers and apply modelling techniques to solve real problems.Acquire the intuition necessary to construct useful and informative models by analysing various examples.Understand the difference between mechanistic and phenomenological/empirical models and their applications.The course slowly builds on the principles required to make useful models of biological dynamics, starting from first principles: (1) Fundamentals of Dynamical Systems in Biology: Introduction to change, dynamics, systems organization, and the role of energy in biological systems.(2) Modelling Molecular Circuits: Using state-transition diagrams to visualize molecular states and transitions.Applying mass-action kinetics to describe the rates of spontaneous molecular reactions and processes within state-transition diagrams.Developing mathematical models based on state-transition diagrams.(3) Net Models and Simplification: Modelling enzyme kinetics, including catalytic cycles, rapid-equilibrium approximations, steady-state methods, and cooperative effects.Developing equilibrium-binding equations for regulatory proteins (e.g., transcription factors, receptors).Reducing complex state-transition diagrams to simpler net process models for use in larger systems.(4) Models of Larger Systems:Applying simplified models to study metabolism, signalling, and signal transduction.Introduction to phenomenological and empirical models for systems where detailed mechanisms are unknown or too complex (e.g., cell growth, ecosystems).(5) Practical Application: Solving exercises using Python and pen and paper to reinforce concepts and build modelling skills.LecturesWorkgroupsSelf-studyComputer practicalsComputer modelling tutorials80% Written exam20% Computer exam (Python)You must have a grade higher than 5.5/10 on both exams to pass.A course syllabus written by the lecturerMaster Bioinformatics and Systems Biology Master MathematicsGenerative AI Policy: In this course, generative AI (GenAI), such as ChatGPT or similar tools, may be used in a limited way, for example for editorial support, rephrasing, or structure. Substantive contributions from GenAI may only be used within the limits set by the lecturer. Any use of GenAI must always be explicitly disclosed, in accordance with the lecturer's instructions. The student remains fully responsible for the content, quality, and accuracy of the submitted work. Incorrect use of GenAI is considered fraud. If established, the submitted work or assessment result will be declared invalid, and the Examination Board may impose further measures.