Dynamic Models: Signalling and Enzyme Kinetics

Lecture
In this lecture, we will move to more complicated examples of mass-action kinetics and use our knowledge of differential equations to describe signalling systems and feedback loops. We will also take a look at enzyme kinetics and the Michaelis-Menten equation, and extend this to be able to model reversible inhibition.
Lecturer

Max de Rooij

Date

February 26, 2025

Slides

13:30 - 15:15 - Dynamic Models: Signalling and Enzyme Kinetics

Slides

Learning Outcomes

Principal Learning Outcome 8

Explain the function of different terms in a simple system of (possibly nonlinear) ordinary differential equations.

Principal Learning Outcome 9

Calculate the steady-state conditions for a simple system of ordinary differential equations.

After this lecture, you should be able to:

  1. Model various stimulatory and inhibitory signalling systems using ordinary differential equations.
  2. Derive the Michaelis-Menten equation from a simple enzyme-substrate reaction.
  3. Explain the terms in the Michaelis-Menten equation and give a biological interpretation of these terms.
  4. Extend the Michaelis-Menten equation to include the three types of reversible inhibition.
  5. Use Hill-type kinetics to model cooperative binding in enzyme kinetics and gene regulation.
  6. Locate and explain positive and negative feedback loops in differential equations.
  7. Calculate the steady-state conditions for a simple system of ordinary differential equations.
  8. Explain the concept of bistability and setpoints in biological systems.

Book Chapters

  • Lecture notes chapter 5