Jrg Ackermann Ina Koch Molecular Bioinformatics Institute of - PowerPoint PPT Presentation

Jörg Ackermann Ina Koch Molecular Bioinformatics Institute of Computer Science Johann Wolfgang Goethe-University Frankfurt am Main j.ackermann@uni-frankfurt.de ina.koch@bioinformatik.uni-frankfurt.de http://www. bioinformatik.uni-frankfurt.de/index.html Sofia, 28th of June 2011

The -omics define different abstraction levels (2 x 10 4 ) (> 10 6 ) (> 10 6 ) (> 10 7 ) Gene regulatory Signal transduction networks networks (2 x 10 3 ) Data: • large and complex • time- and location-dependent • incomplete Metabolic • redundant and changing termini networks Adapted from R.E. Gerszten and T.J. Wang. Nature (2008) 451 :949 – 952

Petri nets in biology Pentose phosphate pathway G6P + 2 NADP + + H 2 O → R5P + 2 NADPH + 2 H + + CO 2 Ribose-5-phosphate Glucose-6-phosphate 2 NADPH NADP + 2 2 H + r H 2 O CO 2

Petri nets in biology Pentose phosphate pathway G6P + 2 NADP + + H 2 O → R5P + 2 NADPH + 2 H + + CO 2 Ribose-5-phosphate Glucose-6-phosphate 2 NADPH NADP + 2 2 H + r H 2 O CO 2 Koch, Reisig, Schreiber (Eds.) (2011) Modeling in Systems Biology – The Petri Net Approach, Springer-Verlag, New York, Berlin

Sucrose-to-starch-pathway in potato tubers Suc + UDP  UDPglc + Frc sucrose synthase: UDP-glucose Pyrophosphorylase: UDPglc + PP  G1P + UTP phosphoglucomutase: G6P  G1P Frc + ATP → F6P + ADP fructokinase: phosophoglucoisomerase: G6P  F6P Glc + ATP → G6P + ADP hexokinase: Suc → Glc + Frc invertase: sucrose phosphate synthase: F6P + UDPglc  S6P + UDP sucrose phosphate phosphatase: S6P → Suc + P i glycolysis (b): F6P + 29 ADP + 28 P i → 29 ATP NDPkinase: UDP + ATP  UTP + ADP sucrose transporter: eSuc → Suc ATP consumption (b): ATP → ADP + P i starch synthesis: G6P + ATP → 2P i + ADP + starch adenylate kinase: ATP + AMP  2ADP pyrophosphatase: PP → 2 P i

eSuc Sucrose transporter Sucrose phosphate Invertase phosphatase Suc UDP Sucrose synthase P i Frc S6P Glc ATP ATP UDPglc Sucrose phosphate synthase Hexokinase Fructokinase ADP ADP UDP F6P PP UDP-glucose Phosphoglucoisomerase Glycolysis 28 pyrophospho- ADP rylase 29 P i 29 ATP ATP Phosphoglucomutase UTP ATP G1P G6P consumption ATP NDPkinase Starch forward UTP synthase ADP ADP UDP 2 P i P i starch ATP ADP backward

Invariant definitions The incidence matrix C = P  T p 1 corresponds to the stoichiometry matrix. t 2 t 3 t 1 t 2 t 3 ( ) 2 p 1 -2 1 1 C = p 2 1 -1 0 p 2 t 1 Steady-state assumption Place (p-) invariant: X = {x 1 , . . . , x m } Transition (t-) invariant: Y = { y 1 , . . . , y m } C T x = 0 C y = 0 – 2 x 1 + x 2 = 0 – 2 y 1 + y 2 + y 3 = 0 x 1 – x 2 = 0 y 1 – y 2 = 0 x 1 = 0

Functional network decomposition T-invariants : minimal non-negative, non-trivial integer solutions minimal: ¬ ∃ invariant z : supp (z) ⊂ supp (x) and gcd { x 1 , . . . , x m } = 1 Petri net interpretation Lautenbach (1973) - set of transitions, whose firing reproduces a given marking - indicate the presence of cyclic firing sequences Biological interpretation - Elementary modes Schuster & Schuster (1993) - based on convex cone analysis - minimal set of enzymes which operate at steady-state - represent basic pathways, reflecting the whole possible steady-state behavior

A successful prediction Glucose Black elementary mode: normal Krebs-cycle Blue elementary mode: catabolic way predicted in Liao et al. (1996) and Schuster et al. (1999). CO 2 Tentative experimental results in Wick et al.(2001). Experimental proof: AcCoA Pyr PEP E. Fischer & U. Sauer: A novel metabolic cycle catalyzes glucose oxidation and anaplerosis Cit Oxac in hungry Escherichia coli, J. Biol. Chem . (2003) 278 : 46446 – 46451 CO 2 IsoCit Gly Mal CO 2 OG Fum Succ SucCoA CO 2

Computational task construct all minimal t-invariants of a network equivalent to get all extreme rays of a convex polyhedral cone           | 0 , 0 P x A x x  unique set of generators of the cone  all operational modes of the network

Two strategies Strategy 1 1.         | 0  Start with cone Q x A x P 0  For each component i generate a new cone          | 0 , Q x x x Q Q  1 i i i i Strategy 2 2.          Start with cone | 0 Q x x P 0   For each row vector generate a new cone A i            | 0 , Q x A x x Q Q  1 i i i i

Problem construct extreme rays of Q i from the extreme rays of Q i-1 lead to “state explosion” task classified to be NP-hard

Application to real-life networks [1] Klee et al. (1972) [2] Pascoletti (1986) [3] Grunwald et al. (2008) [4] MolBI model (unpublished) [5] Herrmann (2006) [6] König (1997)

Run time differences CPU run times of computation of t-invariants (AMD I3 Processor, 3 GHz, 4 GB RAM, 64 bit Suse 11.4); Bold-faced times indicate the fastest methods; a failed, b stopped [1] Starke (1990), Roch & Starke (1999) [2] Lehrack (2006) [3] Schuster et al. (1993) [4] Ackermann (2010) according Colom & Silva (1991)

Conclusions  Computation of all t-invariants is an important task in analyzing biological networks  Various methods and implementations show significantly different efficiencies in practical applications  There is room for improvements

Outlook  Test of more programs for even larger networks of practical relevance  Development of new methods efficient for biological networks  Start competition with other groups to extend the applicability of algorithms to greater biological networks

Acknowledgements to the MolBI - group www. bioinformatik.uni-frankfurt.de/index.html Благодаря