1. Biological Network Analysis: Introduction to Metabolic Networks Tomer Shlomi Winter 2008

2. Lecture Outline 1. Cellular metabolism 2. Metabolic network models 3. Constraint-based modeling 4. Optimization methods

3. 1. Cellular metabolism

4. Metabolism (I) Metabolism is the totality of all the chemical reactions that operate in a living organism. Catabolic reactions Breakdown and produce energy Anabolic reactions Use energy and build up essential cell components

5. Metabolism (II) “Metabolism is the process involved in the maintenance of life. It is comprised of a vast repertoire of enzymatic reactions and transport processes used to convert thousands of organic compounds into the various molecules necessary to support cellular life” Kenneth et al. 2003

6. Why study metabolism? (I) 1.Basic science - it’s the essence of life.. 2.Tremendous importance in Medicine a.In born errors of metabolism cause acute symptoms and even death on early age b.Metabolic diseases (obesity, diabetics) are major sources of morbidity and mortality. c. Metabolic enzymes and their regulators gradually becoming viable drug targets

7. Why study metabolism? (II) 3. Bioengineering applications a.Design strains for production of biological products of interest b.Generation of bio- fuels 4. Probably the best understood of all cellular networks: metabolic, PPI, regulatory, signaling

8. Metabolites and Biochemical Reactions Metabolite - an organic substance: –Sugars – glucose, galactose, lactose, etc’ –Carbonhydrates – glycogen, glucan, etc’ –Amino-acids – histidine, proline, methionine, etc’ –Nucleotides – cytosine, guanine, etc’ –Lipids –Chemical energy carriers – ATP, NADH, etc’ –Atoms – oxygen, hydrogen Biochemical reaction: the process in which one or more substrate molecules are converted (usually with the help of an enzyme) to product molecules Glucose + ATP Glucokinase Glucose-6-Phosphate + ADP

9. Metabolic Networks A set of reactions and the corresponding metabolites A directed hyper-graph representation –Nodes - represent metabolites –Edges - represent biochemical reactions

10. 18. Lecture WS 2008/09 Metabolites (I) The 744 reactions of E.coli small-molecule metabolism involve a total of 791 different substrates. On average, each reaction contains 4.0 substrates. Number of reactions containing varying numbers of substrates (reactants plus products).

11. 18. Lecture WS 2008/09 Bioinformatics III11 Each distinct substrate occurs in an average of 2.1 reactions. Metabolites (II)

12. Reactions Catalyzed by More Than one Enzyme Diagram showing the number of reactions that are catalyzed by one or more enzymes. Most reactions are catalyzed by one enzyme, some by two, and very few by more than two enzymes. For 84 reactions, the corresponding enzyme is not yet encoded in EcoCyc. What may be the reasons for isozyme redundancy? (2) the reaction is easily „invented“; therefore, there is more than one protein family that is independently able to perform the catalysis (convergence). (1) the enzymes that catalyze the same reaction are homologs and have duplicated (or were obtained by horizontal gene transfer), acquiring some specificity but retaining the same mechanism (divergence)

13. Enzymes that catalyze more than one reaction Genome predictions usually assign a single enzymatic function. However, E.coli is known to contain many multifunctional enzymes. Of the 607 E.coli enzymes, 100 are multifunctional, either having the same active site and different substrate specificities or different active sites. Number of enzymes that catalyze one or more reactions. Most enzymes catalyze one reaction; some are multifunctional. The enzymes that catalyze 7 and 9 reactions are purine nucleoside phosphorylase and nucleoside diphosphate kinase.

14. 18. Lecture WS 2008/09 Bioinformatics III14 Pathways (I) EcoCyc describes 131 pathways: energy metabolism nucleotide and amino acid biosynthesis secondary metabolism Pathways vary in length from a single reaction step to 16 steps with an average of 5.4 steps. Length distribution of EcoCyc pathways Ouzonis, Karp, Genome Res. 10, 568 (2000)

15. Pathways (II) However, there is no precise biological definition of a pathway. The partitioning of the metabolic network into pathways (including the well- known examples of biochemical pathways) is somehow arbitrary. These decisions of course also affect the distribution of pathway lengths.

16. Pathway in the Context of a System

17. Reactions participating in more than one pathway The 99 reactions belonging to multiple pathways appear to be the intersection points in the complex network of chemical processes in the cell. E.g. the reaction present in 6 pathways corresponds to the reaction catalyzed by malate dehydrogenase, a central enzyme in cellular metabolism. The 99 reactions belonging to multiple pathways appear to be the intersection points in the complex network of chemical processes in the cell. E.g. the reaction present in 6 pathways corresponds to the reaction catalyzed by malate dehydrogenase, a central enzyme in cellular metabolism.

18. 2. Metabolic Network Models

19. Metabolic Network Models The application of computational methods to predict the network behavior usually requires additional data other than the network topology A ‘GS metabolic network model’ is a collection of such data: –Reaction stoichiometry –Reaction directionality –Cellular localization –Transport and exchange reactions –Gene-protein-reaction association

20. Metabolic Network Model: Reaction Stoichiometry Stoichiometry - the quantitative relationships of the reactants and products in reactions 1 Glucose + 1 ATP 1 Glucose-6-Phosphate + 1 ADP

21. Metabolic Network Model: Reaction Directionality Biochemical studies may test the reversibility of enzymatic reactions But the directionality can differ between in vitro and in vivo due to different temperature, pH, ionic strength, and metabolite concentrations. A subset of the reactions in a model is uni-directional and the remaining reactions are bi-directional 1 Glucose + 1 ATP -> 1 Glucose-6-Phosphate + 1 ADP

22. Metabolic Network Model: Cellular Localization (I)

23. Metabolic Network Model: Cellular Localization (II) Algorithms: PSORT and SubLoc to predict the cellular localization of proteins based on nucleotide or amino acid sequences High-throughput experimental approaches such as immunofluorescence and GFP tagging of individual proteins. Cytoplasm: 1 Glucose + 1 ATP -> 1 Glucose-6-Phosphate + 1 ADP

24. Metabolic Network Model: Transport and Exchange Reactions An extra-cellular compartment is also included in the model Transport reaction move metabolites between compartments (across membrane boundaries) –Glucose[c] Glucose[e] Exchange reaction move metabolites across the model boundary –Glucose[e] Uptake = in Secretion = out

25. Gene-Protein-Reaction (GPR) Association (I) Formulated via Boolean logic Sdh protein made up of 4 peptides, catalyzes 2 reactions

26. Gene-Protein-Reaction (GPR) Association (II) A protein complex made up of 3 proteins catalyzes a single reaction

27. Gene-Protein-Reaction (GPR) Association (III) Isozymes – alternative enzymes that catalyze the same reaction

28. Metabolic Network Models A ‘GS metabolic network model’ is a collection of: –A metabolic network –Reaction stoichiometry –Reaction directionality –Cellular localization –Transport and exchange reactions –Gene-protein-reaction association

29. Model Reconstruction Process (I)

30. Model Reconstruction Process (II) Performed mainly in Bernhard Palsson’s lab in UCSD. Model naming convention:

31. Reconstruction of E. coli models

32. Available Metabolic Models

33. 3. Kinetic modeling

34. Stoichiometric Matrix (I) Stoichiometric matrix – network topology with stoichiometry of biochemical reactions (denoted S) A Metabolite that exists in multiple compartments is represented with multiple rows in the matrix How would transport and exchange reactions represented?

35. Stoichiometric Matrix (II)

36. Kinetic Modeling: Definition Predict changes in metabolite concentrations m – metabolite concentrations vector- mol/mg S – stoichiometric matrix v – reaction rates vector- mol/(mg*h) Reaction rate equationKinetic parameters Requires knowledge of m, f and k! A set of Ordinary Differential Equations (ODE)

37. Kinetic Modeling: Reaction Rate Equations (I) Consider the reaction: S->P A simple rate equation (Michaelis-Menten) is: In this case, we have only 2 kinetic parameters – v max and K m

38. Kinetic Modeling: Reaction Rate Equations (II) Consider the reaction: S + E P + E A more complex Michaelis-Menten equation: In this case, we have only 4 kinetic parameters – v max+, v max-, K mS, and K mP,

39. Kinetic Modeling: Reaction Rate Equations (III) Reaction rate equations also depends (via k) on: –Regulation: effectors, inhibitors –Enzyme concentration –Surrounding reactions and molecules –pH, ion-balance, molecule-gradients, energy potentials Kinetics are problematic –Obtained from test tube tests of purified enzymes –Measurement doesn’t apply on cell environment Most of these parameters are unknown!

40. 4. Constraint-based modeling

41. Constraint-based modeling (CBM) (I) Assumes a quasi steady-state –No changes in metabolite concentrations (within the system) –Metabolite production and consumption rates are equal Representing the ‘average’ flow in the network over a long enough period of time The reaction rate vector v is referred to as a ‘steady-state flux distribution’ No need for information on metabolite concentrations, reaction rate equations, and kinetic parameters

42. CBM (II) Solution space Correct solutions In most cases, S is underdetermined, and there exist a space of possible flux distributions v that satisfy: The idea in CBM is to employ a set of constraints to limit the space of possible solutions to those more likely/correct –Mass balance is enforced by the above equation –Thermodynamic: irreversibility of reactions –Enzymatic capacity: bounds on enzyme rates –Availability of nutrients

43. CBM (III) The solution space decreases with the addition of more constraints Mass balance S·v = 0 Subspace of R Thermodynamic v i > 0 Convex cone Capacity v i < v max Bounded convex cone n

44. CBM Example (I)

45. CBM Example (II)

46. CBM Example (III)

47. Determination of Likely Flux Distributions In most cases lack of constraints provide a space of solutions How to identify plausible solutions within this space? Optimization methods (next lesson) –Maximal biomass production rate –Minimal ATP production rate –Minimal nutrient uptake rate Exploring the solution space (the following lesson) –Extreme pathways –Elementary modes

48. 4. Optimization methods

49. Flux Balance Analysis (I) An optimization method for finding a feasible flux distribution that enables maximal growth rate of the organism Based on the assumption that evolution optimizes microbes growth rate To enable maximal growth rate the essential biomass precursors (metabolites) should be synthesized in the maximal rate Add to the model a pseudo ‘growth reaction’ representing the metabolites required for producing 1g of the organism’s biomass These precursors are removed from the metabolic network in the corresponding ratios: 41.1 ATP + 18.2 NADH + 0.2 G6P… -> biomass

50. For example: Biomass reaction of E. coli

51. Other Possible Objective Functions

52. Flux Balance Analysis (II) Searches for a steady-state flux distribution v: Satisfying thermodynamic and capacity constraints: S∙v=0 v min ≤v ≤v max With maximal growth rate Max v biomass

53. Flux Balance Analysis (II) Searches for a steady-state flux distribution v: Satisfying thermodynamic and capacity constraints: S∙v=0 v min ≤v ≤v max With maximal growth rate Max v biomass How do we find this flux distribution v? Linear Programming

54. Linear Programming Basics (I)

55. Linear Programming Basics (III)

56. Linear Programming: Types of Solutions (I)

57. Linear Programming: Types of Solutions (II)

58. FBA and LP: Single solution Assume that b2 is the ‘biomass’ reaction which we maximize Let b1≤5 (i.e. the maximal uptake rate of A is bounded by 5) One optimal solution exist in which b2=5

59. FBA and LP: Unbounded Assume that b2 is the ‘biomass’ reaction which we maximize Let b1≤∞ (i.e. the maximal uptake rate of A is unbounded) No optimal solution exist B2 can be as high as we want

60. FBA and LP: Solution space (I) Assume that b2 is the ‘biomass’ reaction which we maximize Let b1≤5 There are many possible optimal solutions in which b2=5 Different solutions reflect the activity of alternative pathways: v1+v2=b1≤5

61. FBA and LP: Solution space (II) The LP solution space is convex! (bounded within the original feasible solution space) v biomass =c S∙v=0 v min ≤v ≤v max Max v biomass =c S∙v=0 v min ≤v ≤v max

62. FBA and LP: Solution space (III) The convex solution space can be further analyze For example, finding the optimal growth solution with minimal nutrient uptake v biomass =c S∙v=0 v min ≤v ≤v max Min v met_uptake

63. References: Price ND, Papin JA, Schilling CH, Palsson BO. 2003. Genome- scale microbial in silico models: the constraints-based approach. Trends Biotechnol 21(4):162-9.