9) Metabolic Control Analysis

Question 1

What is a structural linear conservation law in a system of chemical reactions

Answer 1

Question 2

How are conservation laws related to eigenvectors in a system of chemical reactions

Answer 2

Question 3

What is the method for discovering conservation laws in a chemical reaction system using the stoichiometric matrix

Answer 3

1. Identify the System: Represent the chemical reactions using a stoichiometric matrix N
2. Augment the Matrix: Append the identity matrix to N and perform Gauss-Jordan elimination to row-reduce the matrix.
3. Read Conservation Laws: From the reduced form, identify rows corresponding to zero entries in the left-hand part. These rows define the conservation laws.
   4.. Solve aN=0: Find all vectors a (row vectors) such that aN=0.
   This involves identifying left eigenvectors of N with eigenvalue

Question 4

How do you interpret the conservation laws after row reduction of the augmented stoichiometric matrix

Answer 4

Conservation laws are derived from rows with zero entries in the left-hand part of the reduced matrix. The right-hand part gives relationships between species concentrations as conservation laws.

Question 5

What is the rank factorisation of a row-reduced, augmented stoichiometric matrix

Answer 5

Question 6

How is the stoichiometric matrix N factored using linear dependence

Answer 6

Question 7

What is the purpose of the link matrix L0 in the factorisation of N

Answer 7