Hypergraphs, Metabolic Networks, Bioreaction Systems. G. Bastin

Transcription

1 Hypergraphs, Metabolic Networks, Bioreaction Systems. G. Bastin

2 PART 1 : Metabolic flux analysis and minimal bioreaction modelling PART 2 : Dynamic metabolic flux analysis of underdetermined networks 2

3 PART 1 : Metabolic flux analysis and minimal bioreaction modelling Growth of CHO cells in a serum-free medium Substrates Glucose CELLS Lactate Alanine Products Glutamine NH4 CO2

4 The basic issue Growth of CHO cells in a serum-free medium Substrates Glucose CELLS Lactate Alanine Products Glutamine NH4 CO2 Question : What is the minimal set of input-output bioreactions? consistent with cell metabolism explaining measurements in the culture medium

5 Outline 1. Metabolic network and stoichiometric matrix 2. Convex basis and elementary pathways 3. From elementary pathways to bioreactions 4. Experimental data and metabolic flux analysis 5. Computation of minimal sets of bioreactions 6. Final remarks

6 Metabolic network inputs outputs intracellular intermediate metabolites

7 Intracellular biochemical reaction

8 Metabolic network Remark 1 : for the sake of clarity, this is a simplified example representing only the metabolism of «energetic substrates» Glucose inputsand Glutamine. Metabolism of amino-acids is not considered. But outputs the methodology applies to more complex networks as we shall see in Part II. intracellular intermediate metabolites

9 Metabolic network Remark inputs2 : Only internal nodes that are at «branching points» (no loss of generality). outputs intracellular intermediate metabolites

10 Glycolysis

11 Metabolic network metabolic flux stoichiometric coefficient

12 Stoichiometric matrix N (= incidence matrix of the network) internal nodes Glucose 6-P Dihydro-Ac-3P Ribose-5-P Glyc-3-P Pyruvate Acetyl-coA Citrate Alpha-ketoglut Fumarate Malate Oxaloacetate Aspartate Glutamate CO2 Metabolic fluxes

13 Stoichiometric matrix N (= incidence matrix of the network) Glucose 6-P Dihydro-Ac-3P Ribose-5-P Glyc-3-P Pyruvate Acetyl-coA Citrate a-ketoglutarate Fumarate Malate Oxaloacetate Aspartate Glutamate CO

14 Stoichiometric matrix N The set of non-negative vectors of the kernel of N is a polyhedral cone in the non-negative orthant

15 Stoichiometric matrix Convex basis The convex basis is the set of edges of the cone matrix E

16 Elementary pathway Metabolic interpretation of convex basis

17 Elementary pathway Remark 3. In the literature, «Elementary pathways» are also called : «Elementary (flux) modes» or «Extreme pathways».

18 Elementary pathway C 6 H 12 O 6! 2 C 3 H 6 O 3

19 Another example

20 From Convex basis to Bioreaction system Nucleotides Substrates Glucose CELLS Lactate Alanine Products Glutamine NH4 CO2

21 Experimental data (batch) Glucose Cell density Lactate NH4 Glutamine Alanine

22 Experimental data (batch) Glucose Cell density Lactate Green dots = exponential growth NH4 Glutamine Alanine

23 Computation of specific consumption and production rates by linear regression Glucose Glutamine Lactate NH4 Alanine Cell density

24 Metabolic flux analysis

25 Metabolic flux analysis

26 Metabolic flux analysis Non-negative decomposition of in the convex basis

27 The 12 equivalent minimal decompositions Exactly five non-zero coefficients in each vector!

28 12 equivalent minimal (sub)sets of bioreactions

29 Density Glucose Glutamine Lactate Alanine Ammonia 34

30 PART 2 : Dynamic metabolic flux analysis of underdetermined networks Case study : Hybridoma cells for production of Immunoglobuline 35

31 Substrates Glucose Glutamine CELLS NH4 Lactate Alanine CO2 Products 36

32 Substrates Glucose Glutamine CELLS NH4 Lactate Alanine CO2 Products Glutamate Serine Arginine Asparagine Aspartate Histidine Leucine Isoleucine Lysine Methionine Phenylalanine Threonine Tryptophan Valine Tyrosine (Proline) (Cysteine) Glycine Immunoglobuline 37

33 Central Metabolism 38

34 Amino-Acids Metabolism 39

35 40

36 Biomass Synthesis Antibody Synthesis 41

37 42

38 Perfusion culture biomass substrate product dx dt = µx DX ds dt = SX + D(S in S) dp dt = P X DP 43

39 DATA batch perfusion 44

40 45

41 Metabolic Flux Analysis Problem biomass substrate dx dt = µx DX ds dt = SX + D(S in S) n x r p x r N (t) =0 N m (t) = m (t) product dp dt = P X DP 0 apple (t) P S = m r = 70 reactions n = 44 internal metabolites p = 22 measurements Underdetermined system! 46

42 N (t) =0 N m (t) = m (t) 0 apple (t) = Again the set of solutions is a pointed polyhedral cone in the positive orthant qx! i f i! i 0, i=1 qx i=1! i =1 edges of the cone

43 N (t) =0 N m (t) = m (t) 0 apple (t) = Again the set of solutions is a pointed polyhedral cone in the positive orthant qx! i f i! i 0, i=1 qx i=1! i =1 edges of the cone = C A Solution intervals min i apple i apple i max r min i =min f ki,k=1,...,q, max i = max f ki,k=1,...,q

44 Results : Glycolysis fluxes 49

45 Results :TCA-cycle fluxes 50

46 Final remarks 1. Dynamical model under pseudo-steady-state assumption of metabolic flux analysis = order reduction by singular perturbation. 2. «Minimal» must be understood as «data compression»: there is no loss of information in the «minimal model» with respect to the initial metabolic network. 3. Combinatorial explosion. In «Zamorano et al., an example of CHO cells where the network involves elementary pathways and leads to equivalent minimal models!. but each minimal model includes only 22 bioreactions and the polyhedral cone for the interval metabolic flux analysis has only 32 edges. Combinatorial explosion of the number of elementary pathways is not an issue because these 22 bioreactions and 32 edges can be computed directly!

47 References A. Provost, G. Bastin, "Dynamical metabolic modelling under the balanced growth condition", Journal of Process Control, Vol. 14(7), 2004, pp F. Zamorano, A. Vande Wouwer, G. Bastin, "A detailed metabolic flux analysis of an undetermined network of CHO cells", Journal of Biotechnology, Vol.150(4), 2010, pp R.M. Jungers, F. Zamorano, V.D. Blondel, A. Vande Wouwer, G. Bastin, "Fast computation of minimal elementary decompositions of metabolic flux vectors", Automatica, Special issue on Systems Biology, Vol. 47(7), 2011, pp S. Fernandes de Souza, G.Bastin, M. Jolicoeur, A. Vande Wouwer, "Dynamic metabolic flux analysis using a convex analysis approach: application to hybridoma cell cultures in perfusion", Biotechnology and Bioengineering, 2016, in press. 52

48 Thank You! 53