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Unformatted text preview: form (−1, 1, 2, 0, . . . , 0).
Reactions are also used to model ﬂow of metabolites into and out of the cell. For example, suppose
that reaction R2 corresponds to the ﬂow of metabolite M1 into the cell, with v2 giving the ﬂow
rate. This corresponds to a second column of S of the form (1, 0, . . . , 0). 147 The last reaction, Rn , corresponds to biomass creation, or cell growth, so the reaction rate vn is
the cell growth rate. The last column of S gives the amounts of metabolites used or created per
unit of cell growth rate.
Since our reactions include metabolites entering or leaving the cell, as well as those converted
to biomass within the cell, we have conservation of the metabolites, which can be expressed as
Sv = 0. In addition, we are given upper limits on some of the reaction rates, which we express as
max = ∞ if no upper limit on reaction rate j is known. The goal is to
v max , where we set vj
ﬁnd the maximum possible cell growth rate (i.e., largest possible value of vn ) consistent with the
Sv = 0,
v v max .
The questions be...
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