James C. Clements: Week 3

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James C. Clements

BIOL398-01/S11:Assignments

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James C. Clements: Week 3 James C. Clements: Week 7 James C. Clements: Week 11
James C. Clements: Week 4 James C. Clements: Week 8 James C. Clements: Week 12

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 + BC
  2. A + BC
  3. A + B ↔ 2C
  4. 2A + 3BC+D

Please note that the symbolis used to denote arrows (reactions) in both directions.

See solutions here

Simulating Reaction Kinetics

  1. E + SESE + 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.

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Simulation of Reaction Kinetics