Genetic modification of flux
(GMF) for flux prediction of
mutants
Kyushu Institute of Technology
Quanyu Zhao, Hiroyuki Kurata
Topics
• Background of computational modeling of
biological systems
• Elementary mode analysis based
Enzyme Control Flux (ECF)
Genetic Modification of Flux (GMF)
Our objectives
Quantitative modeling of metabolic
networks is necessary for computer-aided
rational design.
Computer model of metabolic systems
Omics data
Molecular Biology data
Integration of heterogenous data
Metabolic Networks
BASE
Genomics
Transcriptomics
Proteomics
Metabolomics
Fluxomics
Physiomics
Quantitative Model
Quantitative Models
Differential equations
Dynamic model，Many unknown parameters
dy
 F (t , x, y , p)
dt
Linear Algebraic equations
0  S v
Constraint based flux analysis at the steady state
FLUX BALANCE ANALYSIS: ＦＢＡ
Prediction of a flux distribution at the steady state
100 v1
X1
v2
X2
v5
Objective function
v3
v4
X3
v6
F ( v)  v5
Constraint
0  S v
 v1 
 
v
 X 1   0   1 1 1 0 0 0   2 
    
  v3 
 X 2    0    0 1 0 1 1 0   v 
 X 3   0   0 0 1 1 0 1  4 
 v 
    
 5 
 v6 
S Stoichiometric matrix
v flux distribution
For gene deletion mutants, steady state
flux is predicted using Boolean Logic
Method
S v  0
Optimization Algorithm
Additional information
rFBA
(regulatory FBA)
Linear Programming
Regulatory network
(genomics)
SR-FBA
(Steady-state Regulatory-FBA)
Mixed Integer Linear
Programming
Regulatory network
MOMA
(Minimization Of Metabolic Adjustment)
Quadratic Programming
Flux distribution of wild type
(fluxomics)
ROOM
(Regulatory On/Off Minimization)
Mixed Integer Linear
Programming
Flux distribution of wild type
Reactions for knockout gene = 0
Other reactions
=1
Current problem:
In gene deletion mutants, many gene expressions
are varied, not digital.
How to integrate transcriptome or proteome into
metabolic flux analysis.
Proposal:
Elementary mode analysis is employed
for such integration.
Elementary Modes (EMAs)
Minimum sets of enzyme cascades consisting
of irreversible reactions at the steady state
EM1
1
v2
v1
A
EM2
B
v3
2
EM1
EM2
 v1 
1
1
 
 
 
 v2   1  1   2  0 
v 
0
1
 3
 
 
Elementary Modes (Ems)
Flux distribution
EM
１
X1
２
３
４
５
v  P
100 v1
40
60
v2
X2
70 v5
30
v3
X3
Coefficients
v6
v4
Elementary mode
matrix
v7
20
Stoichiometric Matrix
30
v1
 X1
v2
X1  X2
v3
X1  X3
v4
X3  X2
v5
X2 
v6
X3 
v7
X2  X3
Flux
1
EM
2 3 4
v  P
5
 v1 
1
1
1
1
 0
 








 
 v2 
1
0
0
1
 0
 v3 
0
1
1
 0
 0
 
 
 
 
 
 
 v4   1  0   2  0   3  1   4  0   5  1 
 v5 
1
0
1
 0
 0
 
 
 
 
 
 
 v6 
0
1
 0
1
 0
0
 0
 0
1
1
v 
 
 
 
 
 
 7
Flux＝ EM Matrix・ EMC
 v1   1
  
 v2   1
 v3   0
  
 v4    0
 v5   1
  
 v6   0
v  0
 7 
1 1 1 0

0 0 1 0
1 1 0 0

0 1 0 1
0 1 0 0

1 0 1 0
0 0 1 1 
100 
1
1
1
1
0


 
 
 
 
 
 60 
1
0
0
1
0
 40 
0
1
1
0
0


 
 
 
 
 
 30   1  0   (1  30)  0   (70  1 )  1   (60  1 )  0   (1  40)  1 
 70 
1
0
1
0
0


 
 
 
 
 
 30 
0
1
0
1
0
 20 
0
0
0
1
 


 
 
 
 
1
EMC is not uniquely determined.
Objective function is required.
 1 
 
 2 
 3 
 
 4 
 
 5
Objective functions
Growth maximization: Linear programming
ne
Max vbiomass   pbiomass , i  i
i 1
Convenient function: Quadratic programming
ne
Max  i2
i 1
Maximum Entropy Principle (MEP)
Maximum Entropy Principle (MEP)
i
psubstrate uptake, i
i 
vsubstrateuptake
 i
Shannon information entropy
n
Maximize   i log i
i 1
n

i 1
i
1
Constraint
n
n
 p
i 1
i
r ,i
 vr
 x
i 1
i r ,i
 vr
 r  1, 2,..., m 
v  P
Quanyu Zhao, Hiroyuki Kurata, Maximum entropy decomposition of flux
distribution at steady state to elementary modes. J Biosci Bioeng, 107: 84-89, 2009
Enzyme Control Flux (ECF)
ECF integrates enzyme activity profiles into
elementary modes.
ECF presents the power-law formula
describing how changes in an enzyme activity profile
between wild-type and a mutant is related to changes
in the elementary mode coefficients (EMCs).
Kurata H, Zhao Q, Okuda R, Shimizu K. Integration of enzyme activities into
metabolic flux distributions by elementary mode analysis. BMC Syst Biol. 2007;1:31.
Enzyme Control Flux (ECF)
Network model with flux of WT
100 v1
40
X1
60
v2
X2
70 v5
30
v3
30
Enzyme activity profile
Mutant / WT
X3
v6
v4
v7
20
Power-Law formula
Estimation of a flux distribution of a mutant
ＥＣＦ Algorithm
v
ref
 P
MEP

ref
ref
Reference model
Power Law Formula
Change in enzyme activity profile

ref

target
(a1 , a2 ,..., an )
Prediction of a flux distribution of a target cell
v
target
 P
target
Power Law Formula

target
i
m
  
ref
i
a
j 1

j, i
Optimal ＝1
 1  EMi
 
1
0
 
0
1
 
0
0
 
 a1 
 
 a2 
1
 
1
 a5 
 
1
1
 
EMi
a1

target
1
 j ,i
a2
a5
Enzyme activity profile
 
ref
1
(a1a2 a5 )
a j (if p j ,i  0)

 1 (if p j ,i  0)
pykF knockout in a metabolic network
19
Glc
1, pts
13, zwf
G6P
20
14, gnd
6PG
18, pgi
glycolysis
Ru5P
16, tktB
21
F6P
29
30
2, pfkA
E4P
GAP
22
15, ktkA
17, talB
Sed7P
3, gapA
23
Pentose
Phosphate
Pathways
PEP
4, pykF
11, ppc
PYR
24
5, aceE
6, pta
AcCoA
Acetate
26
25
OAA
28
12, mez
7, gltA
74 EMs
ICT
10, mdh
TCA cycle
MAL
8, icdA
AKG
9, sucA
27
Effect of the number of the integrated enzymes
on model error (ECF)
30
Model Error
25
20
15
10
5
0
2
4
6
8
10
Number of Integrated Enzymes
An increase in the number of integrated enzymes enhances
model accuracy.
Model Error = Difference in the flux distributions between WT and a mutant
Prediction accuracy of ECF
Gene deletion
Number of
enzymes used for
prediction
Prediction accuracy
(control: no enzyme activity
profile is used)
pykF
11
+++
ppc
8
+++
pgi
5
+
cra
6
+++
gnd
4
+
fnr
6
+++
FruR
6
+++
Summary of ECF
ECF provides quantitative
correlations between enzyme
activity profile and flux distribution.
Genetic Modification of Flux
Quanyu Zhao, Hiroyuki Kurata, Genetic modification of flux for
flux prediction of mutants, Bioinformatics, 25: 1702-1708, 2009
Prediction of Flux distribution for genetic mutants
Metabolic networks
/gene deletion
Metabolic flux
distribution
Gene expression
(enzyme activity) profile
ECF
Metabolic flux distribution for genetic mutants
MOMA/rFBA
Flow chart of GMF
Metabolic networks
/genetic modification
Metabolic flux distribution
mCEF
Gene expression
(enzyme activity) profile
ECF
Metabolic flux distribution for genetic mutants
Expected advantage of GMF
• Available to gene knockout,
over-expressing or under-expressing
mutants
• MOMA/rFBA are available only for gene
deletion, because they use Boolean Logic.
Control Effective Flux (CEF)
Transcript ratio
of metabolic genes
cefi ( s 2)
i ( s1, s 2) 
cefi ( s1)
CEFs for different substrates
glucose, glycerol and acetate.
Transcript ratio for the growth on glycerol
versus glucose
Stelling J, et al, Nature, 2002, 420, 190-193
mCEF is an extension of CEF

available for
Genetically
modification mutants
Up-regulation
Down-regulation
Deletion

m
j ,CELLOBJ
pCELLOBJ , j  EAj
 p
i, j
i
i

 EAPi (if reaction i is modified)
i  
1 (if reaction i is not modified)
mCEFi (mut ) 
1
 
j
max
pCELLOBJ
m
j ,CELLOBJ

 pi , j i
m
j ,CELLOBJ
j
mCEFi ( w) 
1
max
CELLOBJ
p
 (

j ,CELLOBJ
j
j
i ( w, mut ) 
mCEFi (mut )
mCEFi ( w)
 pi , j )
j ,CELLOBJ

GMF = mCEF+ECF
S (Stoichiometric matrix)
P (EMs matrix)
WT
mCEF
vw = P   w
i ( w, m) 
λ   λ
m
i
Mutant
n
w
i

p 1
mCEFi (m)
mCEFi ( w)
p
mCEF
vm = P   m
ECF
Experimental data
mCEF predicts the transcript ratio of
a mutant to wild type
Ishii N, et al.
Science 316 : 593-597,2007
Characterization of GMF
Comparison of GMF(CEF+ECF)
with FBA and MOMA
for E. coli gene deletion mutants
• FBA
Maximize vbiomass
Vk is the flux of gene
knockout reaction k
subject to S  v  0
vk  0
vi  [vi ,min , vi ,max ]
• MOMA
i  1,..., n
N
Minimize  ( wi  xi ) 2
i 1
subject to S  v  0
vk  0
vi  [vi ,min , vi ,max ]
i  1,..., n
Vk is the flux of gene
knockout reaction k
Prediction of the flux distribution
of an E. coli zwf mutant by GMF,
FBA, and MOMA
Zhao J, Baba T, Mori H,
Shimizu K.
Appl Microbiol Biotechnol.
2004;64(1):91-8.
Prediction of the flux distribution
of an E. coli gnd mutant by
CEF+ECF, FBA, and MOMA
Zhao J, Baba T, Mori H,
Shimizu K.
Appl Microbiol Biotechnol.
2004;64(1):91-8.
Prediction of the flux distribution
of an E. coli ppc mutant by
CEF+ECF, FBA, and MOMA
Peng LF, Arauzo-Bravo MJ,
Shimizu K.
FEMS Microbiol Letters,
2004, 235(1): 17-23
Prediction of the flux distribution
of an E. coli pykF mutant by
CEF+ECF, FBA, and MOMA
Siddiquee KA, Arauzo-Bravo
MJ, Shimizu K.
Appl Microbiol Biotechol
2004, 63(4):407-417
Prediction of the flux distribution
of an E. coli pgi mutant by
CEF+ECF, FBA, and MOMA
Hua Q, Yang C, Baba T,
Mori H, Shimizu K.
J Bacteriol 2003,
185(24):7053-7067
Prediction errors of FBA, MOMA and
GMF for five mutants of E. coli
Method
zwf
gnd
pgi
ppc
pykF
FBA
18.38
14.76
23.68
29.92
21.10
MOMA
18.06
14.27
29.38
19.79
25.83
GMF
6.43
9.21
18.47
18.95
20.46
Model Error = Difference in the flux distributions between WT and a mutant
Is GMF applicable to
over-expressing or less-expressing
mutants?
(FBA and MOMA are not applicable to these
mutants.)
Up/down-regulation mutants
FBP over-expressing mutant of C. glutamicum
G6P dehydrogenase over-expressing mutant of C. glutamicum
gnd deficient mutant of C. glutamicum
G6P dehydrogenase over-expressing mutant of E. coli
Summary of GMF
• mCEF is combined to ECF for the accurate
prediction of flux distribution of mutants.
• GMF is applied to the mutants where an
enzyme is over-expressed, less-expressed.
It has an advantage over rFBA and MOMA.
Conclusion
• ECF is available for the quantitative
correlation between an enzyme activity
profile and its associated flux distribution
• GMF is a new tool for predicting a flux
distribution for genetically modified
mutants.
Thank you very much
n
EA j 
 ge
i, j
i 1
 EAPi (if the i-th reaction is involved in the j -th EM)
gei , j  
1 (if the i-th reaction is not involved in the j -th EM)