Metnet_kinetic+models

# Metnet_kinetic+models - Introduction to Enzyme Kinetics for...

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Introduction to Enzyme Kinetics for Metabolic Modeling Concepts • Enzyme Kinetics, Michaelis-Menten equation • Transcription (Repression and Induction) Applications Modeling small-scale biological processes Introduction to Steady State Metabolic Modeling Reading (this week) Section 2.1 in text

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Michaelis-Menten Kinetics • Enzyme not used up • Based on the law of mass action • Derived from the assumptions of free diffusion and thermodynamically-driven random collision. Image: Tom Vickers Steps for finding rate equations 1. Draw a diagram with concentrations of key substrates, products and intermediate complexes 2. Write down the concentration rates of change using flows 3. Use the law of mass action to get flows with respect to the kinectic rate constants
Michaelis-Menten Kinetics • Start with the flows Image: Tom Vickers v 1 1 12 2 dS v dt dE vv dt dES dt dP v dt =− =− + = +− = dS dP v dt dt = Overall flow: v 2 Michaelis-Menten Kinetics • From the Law of Mass Action: Image: Tom Vickers k 2 k 1 k -1 () 11 2 2 2 dS kES k ES dt dE kES dt dES dt dP dt + =+ = i i i

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Michaelis-Menten Kinetics • From the Law of Mass Action: Image: Tom Vickers k 2 k 1 k -1 () 11 2 2 2 dS kES k ES dt dE kES k k ES dt dES k dt dP dt =− + + + + = i i i Assumptions • Quasi-equilibrium assumption: – Time to create ES (complex) is much faster than product creation • Quasi-Steady State (Briggs and Haldane, 1925) – Period in reaction where ES concentration is constant – Only makes sense when S>>E 2 , kk k ± 0 dES dt =
Simplify equations • Use quasi-steady state • Also, recall that the total amount of enzyme, E, is not used up: 0 total dES dE EE E S o r dt dt =+ + = () 11 2 2 2 dS

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Metnet_kinetic+models - Introduction to Enzyme Kinetics for...

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