This preview shows page 1. Sign up to view the full content.
Unformatted text preview: tion
rates, or cell growth, for example.
We focus on m metabolites in a cell, labeled M1 , . . . , Mm . There are n reactions going on, labeled
R1 , . . . , Rn , with nonnegative reaction rates v1 , . . . , vn . Each reaction has a (known) stoichiometry,
which tells us the rate of consumption and production of the metabolites per unit of reaction rate.
The stoichiometry data is given by the stoichiometry matrix S ∈ Rm×n , deﬁned as follows: Sij
is the rate of production of Mi due to unit reaction rate vj = 1. Here we consider consumption
of a metabolite as negative production; so Sij = −2, for example, means that reaction Rj causes
metabolite Mi to be consumed at a rate 2vj .
As an example, suppose reaction R1 has the form M1 → M2 + 2M3 . The consumption rate of M1 ,
due to this reaction, is v1 ; the production rate of M2 is v1 ; and the production rate of M3 is 2v1 .
(The reaction R1 has no eﬀect on metabolites M4 , . . . , Mm .) This corresponds to a ﬁrst column of
S of the...
View Full Document
This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
- Fall '13
- The Aeneid