Kyushu Institute of Technology
Quanyu Zhao, Hiroyuki Kurata

• Background of computational modeling of biological systems
• Elementary mode analysis based
Enzyme Control Flux (ECF)
Genetic Modification of Flux (GMF)

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
Quantitative Model Metabolic Networks
BASE
Genomics
Transcriptomics
Proteomics
Metabolomics
Fluxomics
Physiomics

Quantitative Models
Differential equations
Dynamic model，Many unknown parameters d y

F x y p dt
Linear Algebraic equations
0
 
Constraint based flux analysis at the steady state

FLUX BALANCE ANALYSIS: ＦＢＡ
100 v1
X1 v2
X2 v5
Prediction of a flux distribution at the steady state v3 v4
X3 v6
Objective function
F
 v
5
Constraint
0
 




X
X
X
1
2
3



  
0

1
0

1
1

0
1 0
1

0
1
0
0
   0 0 1

1 0

1

 v v
2 v
 
  v v
6
5
 
S Stoichiometric matrix v flux distribution

For gene deletion mutants, steady state flux is predicted using Boolean Logic
Method 0 Optimization Algorithm Additional information rFBA
(regulatory FBA)
SR-FBA
(Steady-state Regulatory-FBA)
Linear Programming Regulatory network
(genomics)
Regulatory network
ROOM
(Regulatory On/Off Minimization)
Mixed Integer Linear
Programming
MOMA
(Minimization Of Metabolic Adjustment)
Quadratic Programming Flux distribution of wild type
(fluxomics)
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 v
2 v
1
A B

1
EM2 v
3

2
EM1 EM2 v v
2
 
 
1
1
 
 
 
 
2
 
 
 

EM
１
２
３
４
５
Elementary Modes (Ems)
100 v1
X1
60 v2
X2
70 v5
40 v3
30 v4 v7
20
X3
30 v6
Flux distribution v
  
Coefficients
Elementary mode matrix
Stoichiometric Matrix v
4 v
5 v
6 v
7 v
1 v
2 v
3

X
1
X
1

X
2
X
1

X
3
X
3

X
2
X
2

X
3

X
2

X
3

Flux
EM
1 2 3 4 5 v
  v
2
  v
 
  v
5 v
6
 

 

1
 
 
 
2
 
 
 
1
 
 
 
 
1
   
 
0
3
 
1  
 
 
 
1
 
0
 
 
4
 
 

 
 
 

5
 
 
 
 
  v
  
Flux ＝ EM Matrix ・ EMC v v v
2
  
   v v
5
   v
7

1 1 1 1 0
1 0 0 1 0
0 1 1 0 0
0 0 1 0 1
1 0 1 0 0
0 1 0 1 0
0 0 0 1 1







3
  
5



100
60



 
 

40


1
 
   
30 0  

 


70


 
 30   
 20 
0
 
 

(

1

30)
 
 
 
 
 

(70
 
1
)
 
 

(60
 
1
)
 
 
 

(

1

40)




0
0
0
 
 




 
 
 
 

0
1 
EMC is not uniquely determined.
Objective function is required.

Objective functions
Growth maximization: Linear programming
Max v biomass
 i ne 

1 p
 
, i
Convenient function: Quadratic programming
Max
 i ne 

1
 i
2
Maximum Entropy Principle (MEP)

Maximum Entropy Principle (MEP)
 i
Constraint
 i
 p v substrateuptake
  i
Shannon information entropy
Maximize
 i n 

1
 log
 i i i n 

1
 i p
,
 v r v
   i n 

1
 i

1 i n 

1
 x i ,
 v r
 r

1, 2,..., m

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.

Network model with flux of WT
100 v1
X1
60 v2
X2
40 v3
30 v4 v7
20
X3
30 v6
70 v5
Enzyme activity profile
Mutant / WT
Power-Law formula
Estimation of a flux distribution of a mutant

ＥＣＦ Algorithm
MEP v ref    ref
Reference model
 ref
Power Law Formula
 ref   target
Change in enzyme activity profile
( ,
1 2
,..., a n
)
Prediction of a flux distribution of a target cell v target
 target

Power Law Formula
 i target
  i ref j m 

1 a

Optimal
 ＝1
1
 
 
 
 
EMi
0
 
 
 
  a
1
5  
 

1 target  
1 ref
( a a a
1 2 5
)
  
 a ( if p j
1 ( if p

0)

0)
EMi a
1 a
2 a
5
Enzyme activity profile

pykF knockout in a metabolic network
19
Glc
1, pts
13, zwf
20 G6P
18, pgi glycolysis
21 F6P
2, pfkA
28
12, mez
6PG
16, tktB
30
E4P
22
3, gapA
GAP
23 PEP
11, ppc 4, pykF
17, talB
PYR 24
AcCoA
5, aceE
25
6, pta
OAA
7, gltA
ICT
10, mdh
TCA cycle
Acetate
8, icdA
14, gnd
Ru5P
15, ktkA
Sed7P
Pentose
Phosphate
Pathways
26
29
74 EMs
MAL AKG 27
9, sucA

Effect of the number of the integrated enzymes on model error (ECF)
30
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 pykF ppc pgi cra gnd fnr
FruR
Number of enzymes used for prediction
11
Prediction accuracy
(control: no enzyme activity profile is used)
+++
8 +++
4
6
5
6
6
+
+++
+
+++
+++

ECF provides quantitative correlations between enzyme activity profile and flux distribution.

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

Metabolic networks
/genetic modification
Metabolic flux distribution mCEF
Gene expression
(enzyme activity) profile
ECF
Metabolic flux distribution for genetic mutants

• Available to gene knockout, over-expressing or under-expressing mutants
• MOMA/rFBA are available only for gene deletion, because they use Boolean Logic.

Transcript ratio of metabolic genes
 i
 i i
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
 i
( , )

 m
 i
 p
  p

EA
  i
 j
EAP i i

 1 (if reaction is not modified) i
( )

1 max p
CELLOBJ
 j

 m
 j
 m
 p
  i
 i

1 max p
CELLOBJ
 j
(

 j

 p ) i
( ) i

WT
Mutant
S (Stoichiometric matrix)
P (EMs matrix)
  w
 i
λ i m λ i w p n 

1
 p
  m
ECF mCEF
 mCEF i i
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 v biomass
0 v k

0 v i

[ v i ,min
, v i ,max
] i

1,..., n
V k is the flux of gene knockout reaction k
• MOMA
Minimize ( w i
 x i i
N 

1
)
2
0 v k

0 v i

[ v i ,min
, v i ,max
] i

1,..., n
V k is the flux of gene knockout reaction k

Zhao J, Baba T, Mori H,
Shimizu K.
Appl Microbiol Biotechnol .
2004;64(1):91-8.

Zhao J, Baba T, Mori H,
Shimizu K.
Appl Microbiol Biotechnol.
2004;64(1):91-8.

Peng LF, Arauzo-Bravo MJ,
Shimizu K.
FEMS Microbiol Letters,
2004, 235(1): 17-23

Siddiquee KA, Arauzo-Bravo
MJ, Shimizu K.
Appl Microbiol Biotechol
2004, 63(4):407-417

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
FBA 18.38
MOMA 18.06
GMF 6.43
gnd
14.76
14.27
9.21
pgi
23.68
29.38
18.47
ppc
29.92
19.79
18.95
pykF
21.10
25.83
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.)

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

• 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.

• 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.

EA j
 n  i

1 ge ge


EAP i
1 (if the -th reaction is not involved in the -th EM)