Challenges of Complexity and Integration in Quantitative Systems Biotechnology

1. Challenges of Complexity and Integration in Quantitative Systems Biotechnology Eberhard O.Voit Department of Biometry and Epidemiology Medical University of South Carolina 1148 Rutledge Tower Charleston, SC 29425 VoitEO@MUSC.edu National Science Foundation 13-14 September 2000

2. Questions of Interest What are the unmet (near term) opportunities and needs associated with using genomic information for phenotype prediction? What are the developments needed in test-bed and high throughput screening systems? What new mathematical tools, or those that can be adopted from other disciplines, are needed to use genomic information for predictive purposes?

3. Opinion Statement Unmet (near-term) opportunities and needs associated with using genomic information arise from the complexity of organisms. Mathematical tools must aid our understanding of complexity. They must facilitate the integration of diverse types of information in conceptual and quantitative frameworks.

4. Characteristics of Complexity Large numbers of components Large number of processes Processes are nonlinear Quantitative changes in parameters cause qualitative changes in response

5. Large Numbers of Components and Processes  Data acquisition seems “under control”  Should be funded from other sources Biologists have accumulated vast information Computer scientists have developed management tools Bioinformatics promises huge increases in new data

6. Nonlinear Processes  Needs effort Simple extrapolation often faulty Cause-and-effect thinking insufficient Superposition not necessarily valid

7. Quantitative Changes in Parameters  Needs effort p <   system moves to steady state p>  system oscillates System responses difficult to predict

8. From Complexity to Understanding  Strategies 1 and 2 should both be pursued; they should complement each other. Strategy 1: Immediately address systems of large size; minimize need for (and consideration of) detail Strategy 2: Develop true understanding of small systems; scale up

9. From Complexity to Understanding Large-Scale Approach (linear networks; clustering) address large numbers add detail Next Level Understanding Complexity scale up address processes in detail Small-Scale Systems (nonlinearities; design principles)

10. Our Approach (Biochemical Systems Theory) Large-Scale Approach (linear networks; clustering) address large numbers Next Level Understanding add detail Complexity scale up address processes in detail Small-Scale Systems (nonlinearities; design principles)

11. Large-Scale Approaches  Need better statistics, noise reduction  Leave algorithms and databanks to industry?  Need effort Multitude of algorithms for sequencing, gene finding, clustering; multitude of databanks Large models: stoichiometric networks, E-cell, Entelos

12. Limitations of Large-Scale Approaches Fail to provide explanations of structural details: Example: Alternative designs Example: Over-expression of genes Example: Yield optimization in biotechnology

13. Alternative Designs (Savageau) X X X X X X a b 1 3 2 1 3 2 Two different regulatory control structures show outwardly equivalent responses to changes in X1. Why didn’t nature eliminate “redundant” designs?

14. Over-Expression of Genes Why are genes that code for enzymes of the same pathway over-expressed at significantly different rates? Clustering cannot explain this observation. EOV and Radivoyevitch (2000) provided explanations based on a detailed biochemical model.

15. Example: Glycolysis in Heat-Shocked Yeast unchanged 5-10 times 10 - 20 times 2 times 3 times V = 17.73 – in X 1 ATP ; X ; X 8 7 + NADPH NADP ADP Glycogen Glucose-6-Phosphate Trehalose X = 1.011 V 2 G6PDH ATP V = 15.946 PFK ADP Fructose-1,6-Phosphate 2 Glycerol X = 9.144 3 2 ADP V 2 V PK GAPD 2 ATP V POL V ATPase V V HK PFK ATP X = 1.1278 + 2 ADP 5 2 ATP Glucose (external) outside inside Glucose (internal) = 0.0345 V = 17.73 HK ATP ADP UDPG = 1.77 V POL = 0.014 2 NADH 2 NAD + V = 1.772 GOL V = 15.06 GAPD 2 NAD + 2 NADH 2 Phosphoenolpyruvate X =0.0095 4 V = 30.12 PK 2 Ethanol

16. Yield Optimization in Biotechnology Goal: Over-express genes/enzymes for increased yield Ruijter et al. failed with intuitively reasonable, biotechnologically well-executed approach. Torres et al. (1996-2000) used Biochemical Systems Theory to prescribe optimal over-expression patterns. They showed that alterations in only one, two or three control variables are ineffective. EOV and Del Signore showed that imprecise over- expression of enzymes does not improve yield.

17. Small-Scale Systems  Discuss Biochemical Systems Theory (BST) in the following Goals: Understand design principles Facilitate up-scaling to large systems Understand integration within and between levels of organization

18. Biochemical Systems Theory . + + n m n m g h a - b = Õ Õ = X X X i 1 , 2 ,..., n ij ij i i j i j = = j 1 j 1 Ordinary differential equations; one for each dependent variable; represent influxes and effluxes as products of power-law functions: dXi /dt = Vi+(X1, …, Xn) – Vi–(X1, …, Xn) becomes S-system: dXi /dt = aiX1gi1X2gi2… Xngin – biX1hi1X2hi2… Xnhin

19. Advantages of BST Representation Very general: Allows for essentially any (smooth) nonlinearity, including stable oscillations, chaos. Steady-state equations linear. Structure permits powerful diagnostics. Structure permits very efficient numerical analysis (PLAS). Structure is readily scaled up to arbitrary size.

20. Steady-State Equations + + n m n m g h a = b = Õ Õ X X i 1 , 2 ,..., n ij ij i j i j = = j 1 j 1 = - = = b a a g h y ln X b ln( / ) ij ij ij i i i i i + + + + + + = = a y a y ... a y a y ... a y b i 1 , 2 ,..., n Define , , . Steady-state equations become + + + + i 1 1 i 2 2 in n i , n 1 n 1 i , n m n m i × + × = A y A y b D D I I Steady state equation:

21. Evaluation of Steady-State Equations Solution (if steady-state point exists): - - 1 1 = × - × × y A b A A y D D D I I Uniqueness depends on rank of . A D Quantities in the equation can be read off directly from system equations. All properties of the system close to st.st. are consequences of this equation. Stability characterized by eigenvalues.

22. System Diagnostics System responses and sensitivities derived from steady-state equation - - 1 1 = × - × × y A b A A y D D D I I b For instance, change in rate constant changes ; strength of effect on yD ¶ y (parameter sensitivities) - 1 = D A D ¶ b Change in an independent variable amplified/attenuated as ¶ y (signal propagation; gains) - D 1 = - × A A D I ¶ y I Algebraic analysis possible (in principle) ; numerical analysis very efficient.

23. System Diagnostics (cont’d) Large sensitivities (and gains) are often signs of problems: System is not robust. Location of large sensitivities (and gains) pinpoint problematic components or subsystems. Iteration between diagnostics and model refinement leads to better (“optimal”?) model. Example: Sequence of models for purine metabolism (Curto et al., 1997, 1998ab; Voit, 2000)

24. Integration Within Levels Why are particular genes over-expressed simultaneously?

25. Integration Within Levels How is gene expression regulated and coordinated?

26. Integration Within Levels How are biochemical pathways regulated and coordinated? Why are biochemical systems designed in a particular fashion? What do we need to know to design biochemical pathways from scratch?

27. Functional Integration Bridging Levels

28. Summary Unmet (near-term) opportunities and needs associated with using genomic information arise from the complexity of organisms. Mathematical tools must aid our understanding of complexity. They must facilitate the integration of diverse types of information in conceptual and quantitative frameworks.