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

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 Jörg Ackermann Ina Koch

The -omics define different abstraction levels

Adapted from R.E. Gerszten and T.J. Wang. Nature (2008) 451:949–952

Data:

• large and complex
• time- and location-dependent
• incomplete
• redundant and changing termini

(2 x 104) (> 106) (> 106) (> 107) (2 x 103) Gene regulatory networks Signal transduction networks Metabolic networks

Petri nets in biology

Pentose phosphate pathway

Glucose-6-phosphate NADP+ H2O Ribose-5-phosphate NADPH H+ CO2

2 2 2

G6P + 2 NADP+ + H2O → R5P + 2 NADPH + 2 H+ + CO2 r

Petri nets in biology

Pentose phosphate pathway

Glucose-6-phosphate NADP+ H2O Ribose-5-phosphate NADPH H+ CO2

2 2 2

G6P + 2 NADP+ + H2O → R5P + 2 NADPH + 2 H+ + CO2 r

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

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

ATP ADP ATP ATP ATP ATP ADP ADP ADP ADP Pi Pi Pi Pi PP Glc Frc F6P UDP UDPglc G1P UTP UDP S6P Suc eSuc starch G6P

Sucrose transporter Invertase Hexokinase Fructokinase Sucrose synthase Glycolysis Sucrose phosphate phosphatase Starch synthase ATP consumption

ATP

Phosphoglucomutase Sucrose phosphate synthase UDP-glucose pyrophospho- rylase NDPkinase

2 29 29 28

Phosphoglucoisomerase

UDP ADP UTP forward backward

Invariant definitions

C =

• 2 1 1

1 -1 0 t1 t2 t3 p2

(

The incidence matrix C = P  T corresponds to the stoichiometry matrix.

)

t1 t2 t3 p1 p2

2

Place (p-) invariant: X = {x1, . . . , xm} Transition (t-) invariant: Y = {y1, . . . , ym}

CT x = 0 C y = 0 –2x1 + x2 = 0 –2y1 + y2 + y3 = 0 x1 – x2 = 0 y1 – y2 = 0 x1 = 0

p1

Steady-state assumption

Functional network decomposition

T-invariants: minimal non-negative, non-trivial integer solutions minimal: ¬ ∃ invariant z : supp (z) ⊂ supp (x) and gcd {x1, . . . , xm} = 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

Glucose AcCoA Cit IsoCit OG SucCoA PEP Oxac Mal Fum Succ Gly Pyr CO2 CO2 CO2 CO2

A successful prediction

Black elementary mode: normal Krebs-cycle Blue elementary mode: catabolic way predicted in Liao et al. (1996) and Schuster et al. (1999). Tentative experimental results in Wick et al.(2001). Experimental proof:

• E. Fischer & U. Sauer:

A novel metabolic cycle catalyzes glucose oxidation and anaplerosis in hungry Escherichia coli,

• J. Biol. Chem. (2003) 278: 46446–46451

Computational task

construct all minimal t-invariants of a network equivalent to get all extreme rays of a convex polyhedral cone

unique set of generators of the cone all operational modes of the network

 

, |         x x A x P

Two strategies

1.

Strategy 1

 Start with cone  For each component i generate a new cone

2.

Strategy 2

 Start with cone  For each row vector generate a new cone

 

i i i i

Q Q x x A x Q    



     , |

1

i

A 

 

i i i i

Q Q x x x Q    



   , |

1

 

P x A x Q    |   

 

P x x Q    |   

Problem

construct extreme rays of Qi from the extreme rays of Qi-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

[1] Starke (1990), Roch & Starke (1999) [2] Lehrack (2006) [3] Schuster et al. (1993) [4] Ackermann (2010) according Colom & Silva (1991)

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

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