Genetic modification of flux (GMF) for flux prediction of

mutants

Kyushu Institute of TechnologyQuanyu 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

Metabolic Networks Quantitative Model

Omics data Molecular Biology data Integration of heterogenous data

BASE

GenomicsTranscriptomicsProteomicsMetabolomicsFluxomicsPhysiomics

Differential equationsDynamic model ， Many unknown parameters

Quantitative Models

Linear Algebraic equations

( , , , ) d

tdt

y

F x y p

0 S v

Constraint based flux analysis at the steady state

S Stoichiometric matrix 　v flux distribution　　　　

Constraint

Prediction of a flux distribution at the steady state

X1

X2

X3

100 v1

v2

v3

v4

v5

v6

1

21

32

43

5

6

0 1 1 1 0 0 0

0 0 1 0 1 1 0

0 0 0 1 1 0 1

v

vX

vX

vX

v

v

5( )F vv

0 S v

Objective function 　　　　　

FLUX BALANCE ANALYSIS: ＦＢＡ

For gene deletion mutants, steady state flux is predicted using Boolean Logic

0S v Method 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 = 0Other 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)

A B1v

3v

1

2

2v

1

2 1 2

3

1 1

1 0

0 1

v

v

v

EM1 EM2EM1

EM2

Minimum sets of enzyme cascades consisting of irreversible reactions at the steady state

X1

X2

X3

100

60

70

20

40 30

v1

v2

v3

v4

v5

v6

v7

30

Elementary Modes (Ems)

Stoichiometric Matrix

1

2

3

4

5

6

7

1

1 2

1 3

3 2

2

3

2 3

v X

v X X

v X X

v X X

v X

v X

v X X

１

２

３

４

５

EM

v P

Flux distribution

Elementary modematrix

Coefficients

1

2

3

4 1 2 3 4 5

5

6

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

v

v

v

v

v

v

v

1

2 1

3 2

4 3

5 4

6 5

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

v

v

v

v

v

v

v

1 1 1 1 1

100 1 1 1 1 0

60 1 0 0 1 0

40 0 1 1 0 0

( 30) (70 ) (60 ) ( 40)30 0 0 1 0 1

70 1 0 1 0 0

30 0 1 0 1 0

20 0 0 0 1 1

1 2 3 4 5

EMC is not uniquely determined.

EMFluxFlux ＝ EM Matrix ・ EMC

v P

Objective function is required.

Objective functions

Growth maximization: Linear programming

Convenient function: Quadratic programming

2

1

ne

ii

Max

,1

ne

biomass biomass i ii

Max v p

Maximum Entropy Principle (MEP)

1

logn

i ii

Maximize

i ,substrate uptake ii i

substrateuptake

p

v

1

1n

ii

,1

1,2,...,n

i r i ri

x v r m

Maximum Entropy Principle (MEP)

,1

n

i r i ri

p v

Shannon information entropy

Constraint

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

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).

Enzyme Control Flux (ECF)

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 Enzyme activity profileMutant / WT

X1

X2

X3

100

60

70

20

40 30

v1

v2

v3

v4

v5

v6

v7

30

Estimation of a flux distribution of a mutant

Power-Law formula

Enzyme Control Flux 　 (ECF)

ref ref v PReference model

Power Law Formula

Change in enzyme activity profile

target target v P

Prediction of a flux distribution of a target cell

ref target

refMEP

1 2( , ,..., )na a a

ＥＣＦ Algorithm

a1 a5a2

,1

mtarget refi i j i

j

a

,

,,

( 0)

1 ( 0)j j i

j ij i

a if p

if p

1

1

0

0

1

0

0

1

2

5

1

1

1

1

a

a

a

1 1 2 5( )target ref1 a a a

EMi

Power Law Formula

EMi

Enzyme activity profile

Optimal ＝ 1

pykF knockout in a metabolic network

74 EMs

Glc

G6P

F6P

GAP

6PG

Ru5P

E4P

Sed7P

PEP

AcCoA

ICT

AKGMAL

OAA

Acetate

PYR

glycolysis

Pentose PhosphatePathways

TCA cycle

1, pts

2, pfkA

3, gapA

4, pykF

5, aceE6, pta

7, gltA

8, icdA

9, sucA

10, mdh

11, ppc

12, mez

18, pgi

13, zwf

15, ktkA

14, gnd

16, tktB

17, talB

19

20

21

22

24

25

29

30

27

28

23

26

Effect of the number of the integrated enzymes on model error (ECF)

5

10

15

20

25

30

0 2 4 6 8 10

Mo

de

l Err

or

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 +++

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

Summary of ECF

Genetic Modification of Flux

Quanyu Zhao, Hiroyuki Kurata, Genetic modification of flux for flux prediction of mutants, Bioinformatics, 25: 1702-1708, 2009

Gene expression (enzyme activity) profile

Metabolic networks/gene deletion

Metabolic flux distribution

Metabolic flux distribution for genetic mutants

ECF MOMA/rFBA

Prediction of Flux distribution for genetic mutants

Flow chart of GMF

Gene expression (enzyme activity) profile

Metabolic networks/genetic modification

Metabolic flux distribution

Metabolic flux distribution for genetic mutants

mCEF

ECF

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 for the growth on glycerol versus glucose

Stelling J, et al, Nature, 2002, 420, 190-193

( 2)( 1, 2)

( 1)i

ii

cef ss s

cef s

Transcript ratio of metabolic genes

CEFs for different substratesglucose, glycerol and acetate.

mCEF is an extension of CEF

(if reaction is modified)

1 (if reaction is not modified)i

i

EAP i

i

, ,

max,

( )1

( )j CELLOBJ i j

ji

CELLOBJ j CELLOBJj

p

mCEF wp

( )( , )

( )i

ii

mCEF mutw mut

mCEF w

,

,

,

CELLOBJ j jmj CELLOBJ

i j ii

p EA

p

, ,

max,

1( )

mj CELLOBJ i j i

ji m

CELLOBJ j CELLOBJj

p

mCEF mutp

available for Genetically modification mutants

Up-regulationDown-regulationDeletion

GMF = mCEF+ECF

m mv = P

( )( , )

( )i

ii

mCEF mw m

mCEF w

S (Stoichiometric matrix)

w wv = P

P (EMs matrix) mCEF

ECFECF

mCEFmCEF

WTWT

MutantMutant

wiλ λ

1

nmi p

p

Experimental data

Ishii N, et al. Science 316 : 593-597,2007

mCEF predicts the transcript ratio of a mutant to wild type

Comparison of GMF(CEF+ECF) with FBA and MOMA for E. coli gene deletion mutants

Characterization of GMF

• FBA

• MOMA

,min ,max

0

0

[ , ] 1,...,

biomass

k

i i i

Maximize v

subject to S v

v

v v v i n

2

1

,min ,max

( )

0

0

[ , ] 1,...,

N

i ii

k

i i i

Minimize w x

subject to S v

v

v v v i n

Vk is the flux of gene knockout reaction k

Vk is the flux of gene knockout reaction k

Prediction of the flux distribution of an E. coli zwf mutant by GM

F, 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 mutantsFBP over-expressing mutant of C. glutamicumG6P dehydrogenase over-expressing mutant of C. glutamicumgnd deficient mutant of C. glutamicumG6P 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

,

1

n

j i j

i

EA ge

,

(if the -th reaction is involved in the -th EM)

1 (if the -th reaction is not involved in the -th EM)i

i j

EAP i jge

i j