Gene Regulatory Network Identification

Korkut Uygun and Yinlun HuangDepartment of Chemical Engineering and

Materials ScienceWayne State University

AIChE Annual National MeetingSan Francisco

November 16-21, 2003

IntroductionThe regulatory network is major unknown in modeling [Gombert and Nielsen, 2000]

Temporal gene expression data is available Can the gene regulatory network be identified from mRNA data?

Inference MethodsCluster analysis

application of Data MiningBoolean networks

on/off gene expression statusbinary regulation rulesdegradation not included in models

Differential modelsContinuous expression levels

Dynamic Analysis ProblemsExisting works consider only mRNA expressionProtein expression is omitted despite:

Both have similar relaxation timesModels without coupled dynamics cannot display complex behavior [Hatzimanikatis and Lee, 1999]

e.g. circadian rhythmsHowever, coupled models cannot be identified solely on mRNA data [Chen et al., 1999]Further, the effect of metabolites on enzymatic activity is not considered

Gene Regulatory Network A simplified overview

mRNA

Metabolic Reactions

Degradation

transcription translation

Feedback loop

Feedback loop

genesenzyme

Inference problemGiven metabolic kinetic equation

Is it possible to identify a kinetic equation for enzyme and mRNA ?

emm ⋅+⋅= EMdtd ΓΓ

reme ⋅+⋅+⋅= REMdtd ΣΣΣ

rer ⋅+⋅= REdtd λλ

Dynamic Cybernetic Modeling

Postulates that the metabolism is evolved to optimize a cellular objectiveEnables modeling the unknown characteristicsProvides new information based on cybernetic optimality

in silico experimentation

DCM: Log-linear Models

Approximate modeling technique that yields simplified power-law kinetic equations [Hatzimanikatis and Bailey, 1997]

z: vector of state variables (e.g. metabolites)q: vector of manipulated var. (e.g. enzymatic activity)

qBzAz ⋅+⋅=dtd

DCM: Cybernetic ProblemCybernetic Model:

s.t.

Penalizes deviations from nominal (maintain homeostasis)System is described by log-linear models

( ) ( )

( ) ( ) ( ) ( )( )∫ ⋅⋅+⋅⋅+

⋅⋅=

f

0

t

t

TT

fffT

)t(.t.r.w

d ttttt21

tt21Jm in

qRqzQz

zSzq

qBzAz ⋅+⋅=dtd

DCM solutionOptimal input profiles (i.e. kinetic equations) given by a state feedback control law:

Gain is the Kalman gain calculated from algebraic Riccati equation

( ) ( ) qBKzAKq ⋅⋅−+⋅⋅−= ∞∞dt)t(d

DCM-inference problemDefine

assume λE, λR are known

Optimal system is:

=rm

z e=q

( ) ( ) ( )

⋅−⋅−⋅−⋅−=

)t()t()t(

)t()t()t(

dtd

RE

RREREMMM

EM

rem

rem

λλ0λKλKΓKΓK

0ΓΓ

Data fit for mRNASystem can be evaluated analyticallyNonlinear Least-Square regression problemmRNA matrices are identified by iterationCan be simplified by diagonalizing the system

Transforms the multi-variable regression to multiple single variable regressions

Glycolytic Pathway [Hatzimanikatis and Bailey, 1997]

Gin

in

HK

G6P

F6P

FdP

2 3PG

2 PEP

2 ETOH

POL

GRO

K1

K2

PFK

GAPD

PYK

AMP+

ATP

2 ADP

AK

ATP

ADPATPase

GRO2 ADP

2 ATP

2 ADP

2 ATP

ADP

ATP

POL

ADP

ATP

Metabolites:Gin- intracellular glucoseG6P- Glucose-6-phosphateF6P- Frucose-6-phosphateFdP- Frucose-1,6-diphosphate3PG- 3- PhosphoglyceratePEP- Posphoenolpyruvate

Enzyme pathway steps:HK- hexokinase PFK- phosphofructokinaseGAPD- glyceraldehyde 3-phospate dehydrogenasePYK- pyruvate kinaseGRO- glycerol productionPOL- polysaccharideproductionATPase- net ATP consumptionAK- adenylate kinaseK1, K2 - equilibrium steps

ReactionActivationInhibition

Glycolytic Pathway

[ ] TA T P a se,mP Y K,mG A P D,mG R O,mP FK,mP O L,mH K,min,m VVVVVVVV=q

Variables and Initial Condition:

Step disturbance: doubled Gin

[ ]ATPPEPFdPPF6=m

Results – Metabolite profiles

______ : the results with DCM, ______ : the profiles with constant enzyme and mRNA levels

-0.5-0.4-0.3-0.2-0.10.00.10.2

0.0 0.2 0.4 0.6 0.8 1.0time (min)

F6P

leve

l

F6P-optimal

F6P-constantenzyme activity

F6P-optimal

F6P-control

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.0 0.2 0.4 0.6 0.8 1.0time (min)

FdP

leve

l

FdP-optimal

FdP-constantenzyme activity

FdP-optimal

FdP-control

-1.01.03.05.07.09.0

11.013.015.0

0.0 0.2 0.4 0.6 0.8 1.0time (min)

PEP

leve

l

PEP-optimal

PEP-constantenzyme activity

PEP-optimal

PEP-control

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

0.0 0.2 0.4 0.6 0.8 1.0

time (min)

ATP

leve

l

ATP-optimal

ATP-constant enzymeactivity

ATP-optimal

ATP-control

Glycolytic Pathway - DiscussionsDynamics are significantly different:

Cybernetic model results display more complex behaviorMore realistic F6P and ATP profiles are observed [based on experimental data from Chassagnole et al., 2002]

Dynamics are faster than expected

Concluding RemarksA DCM framework for gene regulatory network

inference is introduced:Simple, suitable for very large problems enables identification of the cellular regulatory network based on mRNA data and metabolite kinetic descriptions cybernetic model is capable of describing the complex responses observed in actual biological phenomena can be extended to include other dynamics

transportation of mRNA to the ribosome possibly enzyme activation

Experimental verification of method is underway

ReferencesChassagnole C, Noisommit-Rizzi N, Schmid JW, MauchK, Reuss M. Biotechnology and Bioengineering 79(1):53-73, 2002. Chen T, He H.L., Church G.M. Proc. Pac. Symp. on Biocomputing 4:29-40. 2002. Galazzo JL, Bailey JE. Enzyme and Microbial Technology 12(3):162-172. 1990. Gombert AK, Nielsen J. 11(2):180-186, 2000. Hatzimanikatis V, Bailey JE. Biotechnology and Bioengineering 54(2):91-104, 1997. Hatzimanikatis V, Lee, K.H. Metabolic Engineering 1:275-281, 1999.