We assume that each edge is oriented from a node of

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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...
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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.

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