VL Netzwerke, WS 2007/08 Edda Klipp 1 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Networks in Metabolism and Signaling Edda Klipp Humboldt University Berlin Lecture 6 / WS 2007/08 Elementary Modes

VL Netzwerke, WS 2007/08 Edda Klipp 2 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Metabolic Networks: Definitions repeated

VL Netzwerke, WS 2007/08 Edda Klipp 3 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Metabolic Networks: Constraints

VL Netzwerke, WS 2007/08 Edda Klipp 4 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Metabolic Networks: Pathways

VL Netzwerke, WS 2007/08 Edda Klipp 5 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Metabolic Networks: Elementary Flux Modes

VL Netzwerke, WS 2007/08 Edda Klipp 6 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Flux Modes: Definitions

VL Netzwerke, WS 2007/08 Edda Klipp 7 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Flux Modes: Example

VL Netzwerke, WS 2007/08 Edda Klipp 8 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Flux Modes and Extreme Pathways

VL Netzwerke, WS 2007/08 Edda Klipp 9 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Elementary Flux Modes: Properties

VL Netzwerke, WS 2007/08 Edda Klipp 10 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Convex Analysis: General Problem

VL Netzwerke, WS 2007/08 Edda Klipp 11 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Schusters Algorithm 1. Start with the tableau I for book-keeping or Schuster, S. et al, 2002, J Math Biol, 45,

VL Netzwerke, WS 2007/08 Edda Klipp 12 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Schusters Algorithm

VL Netzwerke, WS 2007/08 Edda Klipp 13 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Schusters Algorithm

VL Netzwerke, WS 2007/08 Edda Klipp 14 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Schusters Algorithm METATOOL

VL Netzwerke, WS 2007/08 Edda Klipp 15 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Pathway Analysis: Application

VL Netzwerke, WS 2007/08 Edda Klipp 16 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Pathway Analysis: Application

VL Netzwerke, WS 2007/08 Edda Klipp 17 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application: Example Network

VL Netzwerke, WS 2007/08 Edda Klipp 18 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application: Example Network

VL Netzwerke, WS 2007/08 Edda Klipp 19 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application: Example Network

VL Netzwerke, WS 2007/08 Edda Klipp 20 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application 1: Pathway Lenghts

VL Netzwerke, WS 2007/08 Edda Klipp 21 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application 1: Pathway Lenghts

VL Netzwerke, WS 2007/08 Edda Klipp 22 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application 2: Optimal Yields

VL Netzwerke, WS 2007/08 Edda Klipp 23 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application 2: Optimal Yields

VL Netzwerke, WS 2007/08 Edda Klipp 24 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application 3: Essential Genes

VL Netzwerke, WS 2007/08 Edda Klipp 25 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application 4: Minimal Cut Sets

VL Netzwerke, WS 2007/08 Edda Klipp 26 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application 4: Minimal Cut Sets

VL Netzwerke, WS 2007/08 Edda Klipp 27 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application 4: Minimal Cut Sets

VL Netzwerke, WS 2007/08 Edda Klipp 28 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EFM Application 4: Minimal Cut Sets

VL Netzwerke, WS 2007/08 Edda Klipp 29 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Elementary Modes: Biological Example Study of redundancy and yield of salvage pathways in human erythrocytes. These cells are not able to synthesize ATP de novo. Instead: the salvage (recycling) of certain nucleosides or bases to give nucleotide triphosphates is operative. As the salvage pathways use enzymes consuming ATP as well as enzymes producing ATP, it is not easy to see whether a net synthesis of ATP is possible. As for pathways using adenosine, a straightforward assumption is that these pathways start with adenosine kinase. However, a pathway bypassing this enzyme and using S-adenosylhomocysteine hydrolase instead was reported. Compute Elementary Flux Modes to compute salvage pathways and stoichiometry of ATP build-up from recycled substrates Salvage – bergen, verwerten

VL Netzwerke, WS 2007/08 Edda Klipp 30 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Erythrocyte Metabolism Model representing glycolysis, the pentose phosphate pathway and purine metabolism in red blood cells, including a methyltransferase and two possible ways of operation of S- adenosylhomocysteine hydrolase (SAHH1 and SAHH2). Transport reactions of adenine and adenosine across the cell membrane are not shown for simplicitys sake. 34 Enzymes 45 Metabolites

VL Netzwerke, WS 2007/08 Edda Klipp 31 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EM Producing ATP from Adenine The ATP glucose yields (that is, the ratios of ATP production over glucose consumption fluxes) of modes II.1-II.4 are 2 : 7, 1 : 6, 1 : 4 and 3 : 10, respectively. Note that these are the yields for the buildup of ATP from adenine rather than from ADP as usually indicated for glycolysis. Mode II.4 has the highest yield.

VL Netzwerke, WS 2007/08 Edda Klipp 32 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EM producing ATP from Adenosine The ATP adenosine yields of the ATP-producing modes are 1 for modes III.1-III.3, 1 : 4, 2 : 5, 1 : 4, 1 : 4, 8 : 17, 5 : 14, 2 : 3, 1 : 4 and 5 : 8 for modes III.4-III.12, respectively. Thus, modes starting from glucose and adenosine transform the latter completely into ATP, which implies that glucose is the only energy source. By contrast, in the modes starting solely from adenosine, part of this substrate is used as an energy source, so that the yield is lower.

VL Netzwerke, WS 2007/08 Edda Klipp 33 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Additional ATP Producing Modes Through SAHH1, but not SAHH2: 12 EM Through SAHH1 and SAHH2: 7 EM Through SAHH2 only: 4 EM In presence of SAHH (but not methyltransferase): 14 EM On the basis of elementary flux modes analysis, it can be said that, even though not easily provable experimentally, the rarely mentioned route via SAHH is rather important. It gives additional opportunities to the cell for generating ATP.

VL Netzwerke, WS 2007/08 Edda Klipp 34 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics A Previously Unknown Metabolic Pathway Glucose AcCoA Cit IsoCit OG SucCoA PEP Oxac Mal Fum Succ Gly Pyr CO 2 Reaction system of 24 reactions: TCA cycle, glyoxylate shunt some amino acid synthesis 26 elementary modes were obtained One EM is a combination of the glyoxylate shunt (isocitrate lyase and malate synthase) with part of the Krebs cycle and involves, in addition, phosphoenolpyruvate (PEP) carboxykinase. Oxaloacetate (OAA) is consumed in equimolar amounts by citrate synthase and PEP carboxykinase. Pathway predicted in Schuster et al. (1999) and similarly in Liao et al. (1996) and later found experimentally (Fischer and Sauer, 2003) ADP + FAD + 4 NAD + 2-phosphoglycerate ATP + FADH2 + 4 NADH + 3 CO2. Overall stoichiometry of that EM:

VL Netzwerke, WS 2007/08 Edda Klipp 35 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EM and Robustness: E.coli Metabolism Robustness and fragility are not predicted by a pure graph-theoretical measure of network topology. In contrast to the network diameter, elementary modes reflect specific characteristics of metabolism such as molar yields. Here: tackled the question whether the number of elementary modes N directly relates to network robustness. As a measure for robustness, they used the maximal growth yield for each mutant. Counting the number of cases for which Y max ( i)>0 gave the number of viable single-gene mutants for each substrate regime, that is, a measure of the probability to tolerate random deletion mutations.

VL Netzwerke, WS 2007/08 Edda Klipp 36 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EM and Robustness: E.coli Metabolism Metabolic network topology and phenotype. a, Relative number of elementary modes N enabling deletion mutants in gene i ( i) of E. coli to grow (abbreviated by ) for 90 different combinations of mutation and carbon source. The solid line separates experimentally determined mutant phenotypes, namely inviability (experiments 1–40) from viability (experiments 41–90). Dashed lines delimit the situations with erroneous predictions. b, Dependency of the mutants maximal growth yield Y max ( i ) (open circles) and the network diameter D( i ) (open squares) on the share of elementary modes operational in the mutants. Data were binned to reduce noise. c, Distribution of growth supporting elementary modes in wild type, that is, share of modes having a specific biomass yield (the dotted line indicates equal distribution). d, Effect of arbitrary single-gene deletions on viability for single substrate uptake (open circles) assessed by the mutants maximal growth yields as in b, but considering the numbers of cases in which Y max ( i)>0, and relating them to the total number of modes for the four substrates in wild type

VL Netzwerke, WS 2007/08 Edda Klipp 37 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics EM and Robustness, E.coli Metabolism

VL Netzwerke, WS 2007/08 Edda Klipp 38 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Caveat 1: Limited Applicability

VL Netzwerke, WS 2007/08 Edda Klipp 39 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Caveat 2: Combinatorial Complexity

VL Netzwerke, WS 2007/08 Edda Klipp 40 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Caveat 2: Combinatorial Complexity

VL Netzwerke, WS 2007/08 Edda Klipp 41 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Caveat 2: Combinatorial Complexity

VL Netzwerke, WS 2007/08 Edda Klipp 42 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Caveat 2: Combinatorial Complexity

VL Netzwerke, WS 2007/08 Edda Klipp 43 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Caveat 2: Combinatorial Complexity Subnetworks from the metabolic networks of T.pallidum. (a) Shows the part of the hierarchy tree that (b) corresponds to. Grey substance names show where shortest paths to the hubs (most connected substances of the network) enter.

VL Netzwerke, WS 2007/08 Edda Klipp 44 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Caveat 3: Feasibility of EFMs?

VL Netzwerke, WS 2007/08 Edda Klipp 45 Max Planck Institute Molecular Genetics Humboldt University Berlin Theoretical Biophysics Caveat 3: Feasibility of EFMs?