3 | Network representation

Question 1

What principle governs reaction balance?

Answer 1

Matter conserved (no creation/loss)

Question 2

What is a reaction vector (r)?

Answer 2

A vector in ℝⁿ, ie in n-dimensional vector space
n = number of metabolites
The vector represents the net metabolite changeWhat is a stoichiometric matrix?
n × m matrix of reaction vectors
Entries are called stoichiometric coefficients

Question 3

What does n represent in a stoichiometric matrix?

Answer 3

n rows representing metabolites

Question 4

What does m represent in a stoichiometric matrix?

Answer 4

m columns representing reactions

Question 5

What two types of reactions in a stoichiometric matrix?

Answer 5

Boundary - either all positive (import) or all negative (export)
Internal - at least 1 negative and 1 positive coefficient

Question 6

Give the stoichiometric matrix of the following reaction network
𝑟1: → 𝐴,
𝑟2: 𝐵 →
r3: 𝐴 → 𝐵

Answer 6

N = [ 1 0 -1, 0 -1 1] (2x3 matrix)

Question 7

There ______ be two biochemical networks with the same stoichiometric matrix!

Answer 7

can

Question 8

Give an example of 2 reaction networks with the same stoichiometric matrix

Answer 8

Network 1:
𝑟1: → 𝐴,
𝑟2: 𝐵 →
r3: 𝐴 → 𝐵
Network 2:
𝑟1: 𝐴→2𝐴,
𝑟2: 2𝐵→𝐵 ,
r3: 𝐴→𝐵,
Both networks represented by the 2x 3 matrix:
N = [ 1 0 -1, 0 -1 1]