Static and dynamic analysis of E. coli metabolic network

1. Static and dynamic analysis of E. coli metabolic network

2. Biochemical pathway: Network of biochemical reactions i.e. metabolites (nodes) “connected” by reactions Note: In living organisms biochemical reactios are (almost) always catalyzed by enzymes

3. Biochemical pathways are usually classified according to their “role”: Signaling pathways Gene regulatory networks Metabolic Pathways We focus on

4. Cellular metabolic pathways: complex networks of interactions Various kind of components: Metabolites; Proteins; Inorganic ions. Various kind of interaction Direct “causation”; +/- feedbacks. Complex, non linear dynamic behaviour e.g. glycolytic oscillations.

5. Computational approaches help in investigating the role played by single components in the behaviour at the system level

6. Computational approaches: Amount of details required Computational power required Interest of many computer scientists Dynamical models: Deterministic Metabolic Control Analysis Metabolic Flux Analysis Stochastic Process calculi based Flux balance analysis: Static network analysis: Pathway logic (Talcott et al. 2002) Biocham (Fages et al.2005) CP(Graph) (Dooms et al. 2000) Palsson et al. since 1995

7. What biologists (usually) want: Solve biological problems:  Organize existing information; Accommodate new information in a coherent framework;  Gain knowledge about systems (predict behaviour in silico);  Drive wet lab experiments (pruning of hypotheses);  ……… (Not necessarily biologists need fully detailed models!)

8. Different approaches towards satisfying biologist needs: Amount of details required Computational power requested Interest of computer scientists Dynamical models: Deterministic Stochastic Flux balance analysis: Static network analysis:

9. Both approaches focus on the same real organism: E.Coli K12 Genome of 4.7x106 bp, including ~ 3200 genes The analysed network: Genome-scale metabolic model (Palsson et al., 2005) including 904 genes

10. Static network analysis approach: tracking causality in metabolic networks Chiara Bodei Davide Chiarugi Andrea Bracciali

11. Determining causal relationships could be non trivial in metabolic networks, e.g.: A B Does A contribute to cause (produce) B ? What happens ifA is removed from the system ?

12. Our approach: Askeletal description language to abstractly specify the clearly understood causal relations amongst the elements composing the network. Tailored simplifications: we are interested in causality only!! In describing biochemical reactions, we abstract away from:  quantities, temperature …….; stoichiometric proportions;  kinetic or thermodynamics parameters; and the dynamical evolution of reactions i.e. we project reactions on a “flat” temporal scale: reactants are not consumed by reactions. This approximated model allow us to effectively perform causality analysis

13. [ APPROACH ] Consider a (bio) chemical reaction, in the classical notation: aA + bB  cC + dD Where: A and B are the reactants, C and D the products and a,b,c,d the Stoichiometric parameters. Under our approximation we obtain: A ￮ B  C ￮ D We call it a rule: the presence of both A and B represents the possibility for C and D to be produced or caused. More precisely, the meaning of this epression would be as: A + B  A + B + C + D We do not consider the dynamic evolution and, therefore, we do not describe reactants consumption

14. [ APPROACH ] The description of causal relationships within a metabolic network can be madebydefining: a set of reaction rules R, as described before, that describe how new metabolites can be produced.  a set I of the metabolites initially present in the experiment Example: The upper part of glycolysis Reaction rules (R) glc6p  fru6p fru6p ° ATP  fru16p ° ADP fru16p ° gap  dhap dhap  gap gap  dhap gap ° nad  bpg13 ° nadh Initial state (I) tglc6p ATP nad

15. [ APPROACH ] Intuitively, given the set R and the set I, we define an explanation for a given metabolite a, the chain of rules that, starting from an (element of) I, leads to a. The existence of an explanation for a gives us indications on the possibility of the production of a. Note that Up to the adequacy of the adopted biological model, the lack of an explanation for a given metabolite represent a strong evidence of the impossibility for that metabolite to be produced in the real case.

16. [ The computational framework] Causal rules, as described, have a straightforward logical interpretation. More specifically, they can be directly translated into Horn Clauses (rules as clauses, and elements in the initial states as facts). A bottom-up semantics allows us to constructively determine the set of reactants that can be produced by the network: Starting from the set of facts I, rules in R are repeatedly applied [i.e. the consequences of the rules whose premises belongs to the set of the possbily produced reactant are added to the set itself] until they are ableto causethe possibility of new reactants. Under the working hypotheses, the process finitely converges to a finite set. The process is correct: a reactant belongs to the computed set iff an explanation for it exists

17. [ IN SILICO EXPERIMENTATION ] In silico gene KO applying the what-if strategy: What happens if a gene coding for an enzyme (and so the enzyme itself) involved in a metabolic network is silenced ? Test set: the metabolic network of E-coli k-12by Palsson and co-workers ( about 600 bio chemical reactions) Our toolkit allows straightforward, one-shot gene KO simulations : :- remove [Rule] removes the reaction(s) catalyzed by the enzime (simulates gene KO) :-Add [Rule] allows to compositionally expand the network :- Check[metabolite]  check whether a metabolite has an explanation We typicaly obtain an answer in a wink !

18. [ IN SILICO EXPERIMENTATION ] What is the price we chose to pay for efficiency ? Recall the approximation: A ￮ B  C ￮ D ~ A + B + C + D (no reactant consumption) This is a heavy approximation of reality: metabolites result producible disregarding the actual availability of reactants But allows to perform quick responsive and reiterable what-if experiments

19. [ IN SILICO EXPERIMENTATION – I ] Mutually essential genes for succinyl-CoA production: Genes sucAB (alpha-ketoglutarate dehydrogenase) and sucCD (succinyl-CoA synthase) of E. coli k-12 could be knocked-outindividually, but notsimultaneously to achieve Succinyl-CoA production. In silico KO: We removed the rules corresponding to the reactions catalyzed by the target enzymes; Outcome: Succinyl-CoA was not produced in silico (i.e. there was no explanation for Succinyl-CoA) only when both the target genes (i.e. the rules corresponding to the action of the encoded enzyme) were simultaneously turned off.

20. [ IN SILICO EXPERIMENTATION - II ] Essential genes for cellular life Extensive in silico gene KO experiments, to test gene essentiality i.e. verifying whether or not in silico knock-out mutants exhibit features typical of living cells: These characteristics could reasonably include: the production of ATP (essential for cellular energetic metabolism); the production of reduced coenzymes NADPH and NADH; structural components, such as the cell wall (murein Biosynthesis). Sample of 114 genesof our set. For each gene: - We removed the rule(s) corresponding to the reaction catalysed by the encoded enzyme - We checked for the presence of the observed elements at the end of each computation. We compared our results with the information contained in the “Geno Base”

21. [ IN SILICO EXPERIMENTATION ] ACCURACY: A = (TP + TN)/(TP + TN + FP + FN) Where: FP  false positives, (the mutant is predicted unviable, but actually lives) FN  false negatives (the mutant is predicted viable, but actually it is not), TP  true positives (both in silico and in vivo mutants are viable) TN  true negatives (both in silico and in vivo mutants are not viable) Our accuracy : 81% Other methods: 60% to 74% (Synthetic accessibility) 62% to 86% (Flux balance analysis, Palsson et al. )

22. Dynamical stochastic approach: tracking dynamical behaviours of whole-cell scale metabolic model Davide Chiarugi Pierpaolo Degano Jan Van Klinken Roberto Marangoni

23. The target biological system: E.Coli K12 The main goal: addressing network dynamics in a whole cell model The analysed network: Genome-scale metabolic model (Palsson et al., 2005) including 904 genes

24. The formalism: a specially tailored subset of π-calculus No restriction Name passing actually not used (synchronization only) Link with biological parameters: Gibbs free energy Activation energy

25. Example: aldolase Dihydroxyacetone-phosphate + D-Glyceraldehyde-3Pβ-D-Fructose 1-6bP becomes product Reactants channel Dihydroxyacetone-phosphate D-Glyceraldehyde-3-P .β-D-Fructose 1-6bP .0 = aldolase<a> = aldolase(x) Formal description of E.coli K12 genome-scale metabolic model (~ 850 reactions and ~ 700 metabolites)

26. In silico esperimentation  Please wait next part of the talk (Jan) for details about the used toolkit  ! Experimental starting conditions: Mimick continuous cultures;  User defined initial quantities of metabolites Virtual experiments: Computations of about 107transitions each

27. Results: • Time course of metabolites concentration reaches the steady-state (homeostasys) as confirmed by regression analysis;  Relative quantities of virtual key metabolites ~ real ones:

28. In silico gene KOs: studying re-routing of metabolic fluxes after gene deletions ppc KO (pep carboxylase) Anaerobiosis, glucose-limited pgi (phosphoglucose isomerase) zwf (glucose-6-P dehydrogenase) Ammonia or glucose-limited

29. Like in real prokaryotes! Results obtained in other works1: Analysis of complex dynamical behaviours glycolytic oscillations When glucose is continuously fed, sustained oscillations emerge…. 1. D. Chiarugi, M. Chinellato, P.Degano, G. Lo Brutto R. Marangoni, CMSB 2006

30. Thank you for your attention !