Biology Reference
In-Depth Information
maximize :
c
τ
i
v
subject to :
S
i
i
v
=
0
v
max
,
where
S
is the stoichiometric matrix containing reaction stoichiometry information,
v
is a vector of all reaction fluxes in the system,
v
min
and
v
max
represent minimum and
maximum constraints on reaction fluxes, respectively, and
c
T
is a vector containing co-
efficients for each flux that is to be maximized (for more detail on FBA, refer to [76]).
The FBA optimization yields an optimal value for the objective along with a fl ux
value for every reaction belonging to the metabolic network. Commonly, FBA is used
to predict maximal growth or metabolite production yields. Cell growth is simulated
by the fl ux over a special “Biomass” reaction that consumes precursors of cellular
components (amino acids, lipids, dNTPs, NTPs, cofactors) and produces a virtual unit
of cell biomass. Maximization of this fl ux is usually set as the FBA objective. This
procedure assumes that organisms have been shaped by the evolution towards growth
maximization, an assumption that has been validated under a variety of conditions
[77].
v
min
≤
v
≤
Flux Variability Analysis
Metabolic networks of living organisms are usually considerably underdetermined
[78-80]. The size of the mathematically allowed flux space can vary depending upon
the network structure and the constraints. The FVA is a method that allows for rough
top estimation of the flux space for a given FBA optimization [41]. The FVA computes
for each reaction an interval of values inside of which the flux of the reaction can
change without influencing value of the objective function, provided that other fluxes
are allowed to vary freely within their constraints.
It is often the case that cells do not operate perfectly optimally when FBA simula-
tions are compared to real data. Therefore, a variant of the FVA approach called sub-
optimal FVA [41] is sometimes informative, wherein instead of fi xing the objective to
its optimal value from the initial FBA run (as in standard FVA), the objective value is
allowed to vary within a predetermined limit. For every suboptimal FVA presented in
this chapter the objective lower limit was chosen at 90% of the initial objective value
(assuming that FBA maximized the objective).
OptKnock
The OptKnock is an approach for identification of mutations that selectively increase
production of a certain compound of interest, assuming that the mutant would optimize
for the same quantity as the wild type (e.g., growth yield) [28]. OptKnock points out
reactions (and genes, through GPR logic) that must be blocked in order to maximize
a linear combination of target fluxes (outer objective) while simultaneously maximiz-
ing for the cell's assumed objective (growth yield; inner objective). OptKnock poses
a bi-level optimization approach that is solved via mixed-integer linear programming
(MILP).
