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

Quantitative Model Metabolic Networks BASE Genomics Transcriptomics Proteomics Metabolomics Fluxomics Physiomics

Quantitative Models

Differential equations Dynamic model，Many unknown parameters

d

y



F

dt

x y p

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

2

X

1 3  1 0    0  1 1 0  1 0 1 0 1  1 0  1 0

v v

2 0 0  1  

v

   

v

4 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) ROOM (Regulatory On/Off Minimization) Linear Programming Mixed Integer Linear Programming MOMA (Minimization Of Metabolic Adjustment) Quadratic Programming Mixed Integer Linear Programming Regulatory network (genomics) Regulatory network Flux distribution of wild type (fluxomics) 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) Flux distribution 100 v1

v

X1 60 v2 X2 70 v5 40 v3 30 v4 v7 20 X3 30 v6  Coefficients Elementary mode matrix Stoichiometric Matrix

v

1

v

2

v

3

v

4

v

5

v

6

v

7 

X 1 X 1



X 1



X 3



X 2



X 3



X 2



X X 3 X X 2 2 3

Flux EM 1 2 3 4 5

v

  2      

v

5

v

6     1         2       3       4       5                                  

v

 Flux ＝ EM Matrix ・ EMC

v

           

v

2 5   

v

7  1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 1 1 0 0 1 1 0 0 0 1 1 0  0 0 1 0 0 1       3 5           100 60 40 30 70 30 20               1      (  1              30)      (70   1 )      (60   1 )      (  1            40)      0 0 0   1 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 

i

log 

i i n

  1 

i p

v



v r



i n

  1 

i

 1

i n

  1 

i x



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.

Enzyme Control Flux (ECF)

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

v

ref

ＥＣＦ Algorithm MEP 

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 1 1 0   0 1 0   EMi 

i target

 

i ref j m

  1

a

 Optimal  ＝1

a a

 

a

1 1 1 1 5   

1 target

  1

ref

(

a a a

1 2 5 )    

a j

(

if p

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 +++ 5 6 4 6 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 

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

) 

i



m



i i



p

 

p



EA

 

i j



EAP i i

  1 (if reaction is not modified) )  1 max

p CELLOBJ



j

 

m



j



m



p

 

i

  1 max

p CELLOBJ



j

(  

j

 

p

) )

i i

WT Mutant

GMF = mCEF+ECF

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 v i

 0  [

v i

,min ,

v i

,max ]

i

 1,...,

n

V k is the flux of gene knockout reaction k • MOMA

Minimize i N

  1 (

w i



x i

) 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

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 FBA MOMA GMF

zwf

18.38

18.06

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.)

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

EA j



n



i

 1

ge ge

 

EAP i

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