Biology Reference
In-Depth Information
OptKnock—modification.
In order to enable the choice of the carbon source(s) the original OptKnock procedure
was modified as follows:
1. A virtual reaction, with limited flux, was created that sourced the virtual com-
pound “vcarbon”
2. For each carbon source a virtual irreversible reaction that converted the com-
pound “vcarbon” into the respective carbon source was added to the model.
The stoichiometry of this virtual reaction corresponded to the number of car-
bon atoms in the carbon source, for example:
6 vcarbon → D-glucose.
3. For each of those reactions (
v
j
) a binary variable (
zj
) defining its activity was
created and following constraint was added to the model:
v
j
≤
v
j
max
z
j
, where
the
v
j
max
was set to value high enough, so that the whole “vcarbon” could be
consumed by each reaction.
This modifi cation allows for the choice of one or more carbon sources that, to-
gether with the mutation set identifi ed by OptKnock, provide the highest objective.
Identification of Minimal Growing Reaction Set
The minimal growing set was identified using a MILP approach, by modifying origi-
nal FBA LP problem. For every non-blocked and non-essential reaction a binary vari-
able was added that reflects the activity of the reaction. When the binary variable
takes value of 1 the corresponding reaction is virtually unlimited (or limited by rules
of original LP problem). When the variable is set to 0 the corresponding reaction is
blocked (non-zero flux is impossible). This was achieved by adding a following set of
equations to the original LP problem:
−
y
i
i
v
i
lim
≤
v
i
≤
y
i
i
v
i
lim
for reversible reactions, and
y
i
i
v
i
lim
v
i
≤
for irreversible reactions. In order to assure that growth was not overly restricted, a
minimal flux value was established for the biomass reaction. We set the lower limit on
biomass flux to 0.05 when the supply of carbon source was 60 mmol
C·
g
DW
−1
h
−1
, which
corresponds to growth yield of 0.07 g
DW·
g
C
−1
, 16 times lower than the wild type. The
objective of the problem was set to minimize the sum of all binary variables
y
i
:
∑
minimize
y
i
.
i
This method searches for a minimal set that is able to sustain growth greater than or
equal to to the minimal growth requirement.
