ENG340/542 Network Modeling, Lecture 6, Hill Laws, Motifs [James Glazier] September 26, 2023

ENG340/542 Biological Network Modeling Lecture 6, Michaelis-Menten and Hill Laws
September 26, 2023
Presented by Prof. James A. Glazier
Indiana University, Department of Intelligent Systems Engineering and Biocomplexity Institute
Bloomington, IN 47408, USA

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

*Contents*
00:07 - Outline
15:22 - Exercise 6.2 Downloading and Converting an SBML Model on Your Own
15:53 - Review: Column Selection and getSteadyStateValues in Tellurium, Using numpy empty(shape), vstack() and hstack() for Parameter Scans
21:44 - Review: Michaelis-Menten Kinetics
24:06 - Review: Cooperative Enzymatic Reactions, Hill Equation
24:48 - Exercise 6.3 Cooperative Reactions (Review). Hill Equation
33:44 - Exercise 6.4 Changing the Exponent in the Hill Equation
42:35 - Properties of Increasing Hill Functions,
51:48 - Decreasing Hill Functions
54:00 - Exercise 6.5 Comparing Hill Equation to Cooperative Dynamics
1:11:28 - Exercise 6.6 Comparing Hill Equation to Cooperative Dynamics with Fixed Substrate Concentrations
1:21:04 - Comparing Hill Equation to Cooperative Dynamics Equilibration Kinetics
1:21:40 - Introduction to Gene Regulatory Motifs
1:25:20 - Modeling an Autocatalyic Network
1:26:48 - Translating Signaling Networks into Rate Equations Using Hill Functions
1:34:14 - Interpreting Gene Regulatory Network Diagrams as Chemical Reactions, Importance of Unwritten Decay Process
1:36:09 - Converting Activating Gene Regulatory Network Diagrams into Rate Equations using Increasing Hill Functions
1:39:22 - Converting Inhibitory Gene Regulatory Network Diagrams into Rate Equations using Decreasing Hill Functions
1:40:36 - Comparing Activation and Inhibition
1:43:07 - Exercise 6.7.1 Autocatalysis: Derive the Rate Equations
1:45:41 - Exercise 6.7.2 Autocatalysis: Write Simulate the Time Series for Different Initial Levels of A, Bistability
1:52:11 - Exercise 6.7.3 Autocatalysis: Determine the Steady States
1:59:20 - Exercise 6.7.4 Autocatalysis: Determine the Dependence of the Steady States on Key Parameters
2:06:00 - Bistability and Bifurcations in Autocatalysis

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