Graph Theory

Lecture
In this lecture, we will introduce graph theory to study biological regulatory systems. In the lecture, we introduce the concept of graphs, and graph properties that can be used to study networked systems.
Lecturer

Max de Rooij

Date

February 14, 2025

Slides

08:45 - 10:30 - Graph Theory

Slides

Learning Outcomes

Principal Learning Outcome 6

Apply concepts of graph theory (connectivity, directionality, cycles, and self-loops) to study metabolic processes and regulation.

After this lecture, you should be able to:

  1. Describe the main principles of biological regulatory systems (emergence, redundancy, modularity) and connect these to the how systems biology can be used to study human metabolism.
  2. Describe the different usage of “models” in systems biology, explain the distinction between “top-down” and “bottom-up” models, and give examples of each.
  3. Explain the concept of a mathematical graph and give examples of graphs encountered in studying systems biology.
  4. Convert a graph into a matrix representation (adjacency matrix) and vice versa.
  5. Explain different types of graphs (directed, undirected, weighted, unweighted, connected, disconnected, cyclic, acyclic, bipartite, and self-looped) and give examples of each.
  6. Calculate various properties of a graph (degree, degree distribution, scale-free, connectedness, hubs, walks, trails, paths, shortest paths) and give a biological interpretation of these properties.
  7. Explain the concept of a metabolic network and give examples of metabolic networks in human metabolism.
  8. Construct the three types of biochemical graph representations (metabolite graphs, reaction graphs, and combined metabolite-reaction graphs) from a metabolic network.
  9. Compute the stoichiometry matrix of a metabolic network.
  10. Explain what data can be used to reconstruct metabolic networks and give confidence levels for different types of data.

Book Chapters

  • Lecture notes chapters 1 and 2