Systems II. Metabolic Cycles

Transcription

1 Systems II Metabolic Cycles

2 Overview Metabolism is central to cellular functioning Maintenance of mass and energy requirements for the cell Breakdown of toxic compounds Consists of a number of major pathways and cycles in order to achieve complex biotransformations Carbon sources (e.g. glucose) converted to precursor metabolites via fueling reactions. Also, energy is generated Glycolysis TCA cycle Biosynthesis: precursor metabolite converted to building blocks amino acids, nucleic acids Polymerization (from building blocks) Proteins, DNA and RNA, carbohydrates, lipids

3 Example TCA Cycle If I vary the input, do I increase the output? Control at levels of Substrate Enzymes Thermodynamics

4 Example Mixed Acid Fermentation How do I increase flux on a particular path?

5 Metabolic Networks

6 Metabolic Networks Databases exist Extensive theoretical development Simple principles (stoichiometry, thermodynamics) lead to rich systems properties

7 Modeling Approaches

8 Metabolic Flux Analysis (MFA) In a network, it is useful to consider reaction fluxes (v i ) rather than explicit reaction kinetics and species concentrations E.g., v1 v2 A B C db [ ] = v1 v2 = 0 (at steady-state) dt MFA: calculation of intracellular fluxes based on measured extracellular fluxes and stoichiometric mass balance models

9 Urea Cycle Overall stoichiometry: CO 2 + NH ATP + aspartate + 2 H 2 O urea + 2 ADP + 2 Pi + AMP + PPi + fumarate

10 Individual reactions Intracellular v1 1: CO + NH + 2ATP + H O C. phos. + 2ADP + P v2 2: C. phos. + ornithine citrulline + P v3 3: citrulline + Asp +ATP arginosuccinate + AMP + PP v4 4: arginosuccinate Arg + fumarate v5 5: Arg + H O urea + 2 ornithine i i i Extracellular v ( ) ex v ( ) ex ( ) ( ) 6 6: Asp Asp 7 7: Arg Arg v8 8: citrulline citrulline ex v9 9: ornithine ornithine ex

11 Intracellular Ornithine and ATP reactions v1 1: CO + NH H O C. phos. + 2ADP + P v2 2: C. phos. + citrulline + P v3 3: citrulline + Asp + arginosuccinate + AMP + PP 4: arginosuccinate 5: Arg + H O 2 ATP ornithine v5 ATP v4 urea Arg + fumarate + ornithine i i i Extracellular v ( ) ex v ( ) ex ( ) ( ) 6 6: Asp Asp 7 7: Arg Arg v8 8: citrulline citrulline ex v9 9: ornithine ornithine ex

12 Form balances on individual metabolites d d [ ornithine] dt [ ATP] dt = v + v + v = 2v v Generalize dc dt = S v c1 [ATP] c [urea] 2 c = c3 = [ornithine] c n c n

13 Stoichiometric matrix S = stoichiometric matrix {S ij } = coefficient of metabolite i in reaction j ATP urea ornithine rxn1 rxn2

14 Measured reaction fluxes How do you calculate the velocity of a thrown baseball? Can measure the flux of extracellular metabolites

15 Partition into Measured and Unknown Fluxes Extracellular metabolites each participate in only one flux not zero 0 intracellular 0 not zero diagonal = extracellular 0 reactions uptake S v= not zero 0 0 diagonal + not zero 0 S= S + S m u likewise v= vm + vu

16 Putting it all together For r = rank{s u } and n = number of unknowns = length (v u ), If r = n, solve exactly If n > r, the system is underdetermined. You need more measurements or relationships If r > n, the system is overdetermined. You solve essentially via least-squares. The extra degrees of freedom can tell you about uncertainty. ( ) ( ) S v= S + S v + v = S v + S v m u m u m m u u ( ) S v = S v = b u u m m

17 Chan et al. What was the goal? Go through tables

18 Experimental Verification- Radiolabeling From amount of 14 CO 2 produced and distribution from [1-14 C] vs. [6-14 C]glucose, can determine PPP flux.

19 Flux Balance Analysis (FBA)

20 FBA Constraints

21 FBA Constraints

22 Example: Prediction of Mutant Behavior

23 Metabolic Pathways: Example

24 Metabolic Pathways: Stochiometric Matrix

25 Elementary Flux Modes (EFMs)

26 EFMs: Simple Example

27 EFMs: Interpretation

28 EFM Applications: Optimal Yields

29 EFM Applications: Optimal Yields

30 Further Reading Metabolic pathways any biochemistry text Web sites of pathways KEGG: MetaCyc: Metabolic Pathways Chart: s/enzyme_explorer/key_resources/metabolic_pathways.ht ml Isotopomer balance Zupke et al., Anal. Chem., 247:287 (1997). All aspects Stephanopoulos, Aristidou and Nielsen, Metabolic Engineering. Principles and Methodologies, Academic Press, 1998.