Gene Regulatory Network Identification

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1 Gene Regulatory Network Identification Korkut Uygun and Yinlun Huang Department of Chemical Engineering and Materials Science Wayne State University AIChE Annual National Meeting San Francisco November 16-21, 2003

2 Introduction The 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?

3 Inference Methods Cluster analysis application of Data Mining Boolean networks on/off gene expression status binary regulation rules degradation not included in models Differential models Continuous expression levels

4 Dynamic Analysis Problems Existing works consider only mrna expression Protein expression is omitted despite: Both have similar relaxation times Models without coupled dynamics cannot display complex behavior [Hatzimanikatis and Lee, 1999] e.g. circadian rhythms However, coupled models cannot be identified solely on mrna data [Chen et al., 1999] Further, the effect of metabolites on enzymatic activity is not considered

5 Gene Regulatory Network A simplified overview Feedback loop genes transcription mrna translation enzyme Degradation Feedback loop Metabolic Reactions

6 Inference problem Given metabolic kinetic equation dm = ΓM m + ΓE e dt Is it possible to identify a kinetic equation for enzyme and mrna? de = ΣM m + ΣE e + ΣR r dt dr = λe e + λr r dt

7 Dynamic Cybernetic Modeling Postulates that the metabolism is evolved to optimize a cellular objective Enables modeling the unknown characteristics Provides new information based on cybernetic optimality in silico experimentation

8 DCM: Log-linear Models Approximate modeling technique that yields simplified power-law kinetic equations [Hatzimanikatis and Bailey, 1997] d z dt = A z + B q z: vector of state variables (e.g. metabolites) q: vector of manipulated var. (e.g. enzymatic activity)

9 DCM: Cybernetic Problem Cybernetic Model: s.t. Penalizes deviations from nominal (maintain homeostasis) System is described by log-linear models ( ) ( ) () () () () ( ) + + = f 0 t t T T f f f T ) ( t w.r.t. dt t t t t 2 1 t t 2 1 J min q R q z Q z z S z q q B z A z + = dt d

10 DCM solution Optimal input profiles (i.e. kinetic equations) given by a state feedback control law: dq(t) dt ( K A) z + ( K B) q = Gain is the Kalman gain calculated from algebraic Riccati equation

11 DCM-inference problem Define assume λ E, λ R are known Optimal system is: = r m z e q = ( ) ( ) ( ) = (t) (t) (t) (t) (t) (t) dt d R E R R E R E M M M E M r e m r e m λ λ 0 λ K λ K Γ K Γ K 0 Γ Γ

12 Data fit for mrna System can be evaluated analytically Nonlinear Least-Square regression problem mrna matrices are identified by iteration Can be simplified by diagonalizing the system Transforms the multi-variable regression to multiple single variable regressions

13 Glycolytic Pathway [Hatzimanikatis and Bailey, 1997] ADP ATP in HK G in ATP ADP ATPase Metabolites: G in - intracellular glucose G6P- Glucose-6-phosphate F6P- Frucose-6-phosphate FdP- Frucose-1,6-diphosphate 3PG- 3- Phosphoglycerate PEP- Posphoenolpyruvate POL GRO G6P POL F6P ADP PFK ATP FdP GRO 2 ADP GAPD 2 ATP 2 3PG K 1 2 PEP K 2 AK AMP + ATP 2 ADP Enzyme pathway steps: HK- hexokinase PFK- phosphofructokinase GAPD- glyceraldehyde 3-phospate dehydrogenase PYK- pyruvate kinase GRO- glycerol production POL- polysaccharideproduction ATPase- net ATP consumption AK- adenylate kinase K 1, K 2 - equilibrium steps Reaction Activation Inhibition 2 ADP 2 ATP PYK 2 ETOH

14 Glycolytic Pathway Variables and Initial Condition: m = [ F6P FdP PEP ATP] q = [ V V V V V V V V ] T m,in m,hk m,pol m,pfk m,gro m,gapd m,pyk m,atpase Step disturbance: doubled G in

15 Results Metabolite profiles F6P level FdP level F6P-optimal F6P-optimal -0.3 F6P-control F6P-constant -0.4 enzyme activity time (min) FdP-optimal FdP-optimal -0.8 FdP-control FdP-constant enzyme activity time (min) PEP level ATP level PEP-optimal PEP-control PEP-optimal PEP-constant enzyme activity time (min) ATP-optimal 1.0 ATP-control ATP-constant enzyme 0.5 activity ATP-optimal time (min) : the results with DCM, : the profiles with constant enzyme and mrna levels

16 Glycolytic Pathway - Discussions Dynamics are significantly different: Cybernetic model results display more complex behavior More realistic F6P and ATP profiles are observed [based on experimental data from Chassagnole et al., 2002] Dynamics are faster than expected

17 Concluding Remarks A 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

18 References Chassagnole C, Noisommit-Rizzi N, Schmid JW, Mauch K, Reuss M. Biotechnology and Bioengineering 79(1):53-73, Chen T, He H.L., Church G.M. Proc. Pac. Symp. on Biocomputing 4: Galazzo JL, Bailey JE. Enzyme and Microbial Technology 12(3): Gombert AK, Nielsen J. 11(2): , Hatzimanikatis V, Bailey JE. Biotechnology and Bioengineering 54(2):91-104, Hatzimanikatis V, Lee, K.H. Metabolic Engineering 1: , 1999.