ENG340/542 Network Modeling, Lecture, 5 Enzyme Kinetics [James Glazier] September 19, 2023

ENG340/542 Biological Network Modeling, Lecture 5, Enzyme Kinetics, Michaelis-Menten and Hill Laws
September 19, 2023
Presented by Prof. James A. Glazier
Indiana University, Department of Intelligent Systems Engineering and Biocomplexity Institute
Bloomington, IN 47408, USA

Engineering 340/542 teaches how to model network dynamics using the Tellurium/Antimony model specification framework and Python-based Jupyter notebooks. The course covers the basics of developing simple metabolic, cell-signaling, gene-regulatory and pharmaco-kinetic network models and fitting models to experimental data. The fifth video discusses how enzymatic reactions can lead to Michaelis-Menten or Hill dependencies of reaction rate on substrate concentration. The video also shows how to use numpy vstack and hstack commands to plot dependencies of reaction rates on concentrations. Since nanoHUB is a free resource, anyone who is interested can create a nanoHUB account and learn along with us.

Main Reference: Herbert Sauro, Systems Biology: Introduction to Pathway Modeling, Chapter 1, 2, 3, Appendix D

*Contents*
00:00 - Outline for the Video
02:07 - Comments on Homework 2--How to Submit Homework
05:18 - How to Describe Results from Dynamic Network Simulations
09:54 - Solving Steady States with Stoichiometry (Homework Problem 2.4)
22:24 - Adjusting Time Scales in Simulations
24:30 - How to Answer Open-Ended Questions
28:04 - Review: Chemical Equilibria and Equilibrium Constants
28:54 - Review: Fixed Points and Steady States
29:55 - Review: Enzymatic Reactions, Boundary Species, $ Notation for Fixed Species
38:39 - Arrow Notation and Unwritten Boundary Species, Converting Diagrams to Rate Equations, Competitive Inhibition
50:40 - Selecting Columns to Output in Tellurium
59:34 - Exercise 5.1 Using Column Selection in Tellurium
1:03:23 - Exercise 5.3 Comparing Enzyme Limitation and Constant Substrate Cases
1:29:43 - Adding Legends to plotArray() Plots using the labels=[] option
1:32:37 - Exercise 5.5 Plotting Steady-State Rates of Production of Product in an Enzymatic Reaction as a Function of Substrate Concentration, Michaelis-Menten Kinetics
1:40:08 - Using Tellurium getSteadyStateValues() with conservedMoietyAnalysis=True, Issues with getSteadyStateValues Function, Running Simulations to Steady-State as an Alternative
1:49:07 - Michaelis Menten Kinetics Arise from Simple Enzymatic Reactions with Mass Action Kinetics
1:54:04 - Derivation of Michaelis Menten Kinetics
1:58:45 - Michaelis Constant
2:01:50 - Michaelis Constant is the Concentration at Which the Rate of Reaction is Half its Maximum Value
2:02:51 - Validity of Michaelis-Menten Rate Law
2:06:49 - Exercise 5.6 Cooperative Reactions and the Hill Equation
2:15:03 - Derivation of the Hill Equation
2:16:55 - Hill Rate Law and Hill Constant (Half-Maximal Concentration), Relation to Michaelis-Menten Rate Law
2:20:30 - v_max in the Hill Equation

If you found this video useful, please check out our other videos teaching computational modeling: