James C. Clements: Week 3

Terminology

• Dynamical System: "A system that changes over time according to a set of fixed rules that determine how one state of the system moves to another state." [1]

• Law of Mass Action: "The law that states the following principle: the rate of a chemical reaction is directly proportional to the molecular concentrations of the reacting substances" [2]

• Homeostasis: "The ability of a system or living organism to adjust its internal environment to maintain a stable equilibrium; such as the ability of warm-blooded animals to maintain a constant temperature." [3]

• Equilibrium: "The condition of a system in which competing influences are balanced, resulting in no net change." [4]

• Oscillation: "A regular periodic variation in value about a mean" [5]

• Autocatalysis: "Catalysis in which the catalyst is one of the products of the reaction" [6]

Applying the Law of Mass Action

• Construct differential equations that model the following reactions. Be sure to define your state variables and rate constants.

1. A + B → C
2. A + B ↔ C
3. A + B ↔ 2C
4. 2A + 3B ↔ C+D

Please note that the symbol ↔ is used to denote arrows (reactions) in both directions.

See solutions here

Simulating Reaction Kinetics

• Use the matlab code provided at my lionshare folder to study the simple reaction

1. E + S ↔ ES → E + P

that we have studied in class. Set the parameters as follows:

• [S₀] = 1.0
• [E₀] = 0.2
• [ES₀] = 0.0
• [P₀] = 0.0
• k₁ = 2.0
• k_-1 = 0.0
• k₂ = 10

Plot the output, and save the plot as an image. Post the image on the wiki as the answer to the question.

Simulation of Reaction Kinetics