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Motivation CSM CSM KaiABC Oscillator KaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11 Membrane Systems Combining Variable Molecular Structures with Discretised Reaction Kinetics From a Toy to a Tool in Systems Biology

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Membrane Systems Combining Variable Molecular Structures with Discretised Reaction Kinetics

From a Toy to a Tool in Systems Biology Thomas Hinze

Friedrich-Schiller University Jena Department of Bioinformatics at School of Biology and Pharmacy thomas.hinze@uni-jena.de

November 25, 2009

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Outline

CSMs with Incomplete Protein Activation Information: KaiABC Oscillator

  • 1. Motivation
  • 2. Cell signalling modules (CSM)
  • 3. P system framework ΠCSM
  • 4. The KaiABC Oscillator: A circadian clock
  • 5. Case Study ΠKaiABC
  • 6. Network reconstruction by artificial evolution
  • 7. The SBMLevolver:

a two-level evolutionary algorithm

  • 8. Evolved networks: a selection
  • 9. Ongoing study: control system-based

specification of circadian oscillators

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze 1 1 1 1 1 1 1 1 1 1 1 1 1

# time

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Combinatorial Explosion of Protein Activation States

  • Tumor suppressor protein p53: 27 phosphorylation sites
  • Up to 227 = 134, 217, 728 distinguishable activation states
  • Each state: individual constituent of reaction network

3 2 1 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

www.rcsb.org/pdb −> education corner 1tsr

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Cell Signalling Module

Characteristics

  • Intracellular reaction network acting as functional unit
  • Composed of proteins carrying phosphorylation sites
  • Interactions between individual activation states

Facts

  • Dynamical behaviour essential to understand function
  • Often partially unknown
  • Reconstruction as challenging task in systems biology
  • Reverse engineering by integrative approach

Idea to manage complexity: Capturing each protein by a specific string-object instead of separate species per activation state

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Specification of String-Objects

Assuming two alphabets: V (for protein names), V ′ (for protein properties); w.l.o.g #, ¬, ∗ / ∈ V ∪ V ′ Syntax for string-objects by regular set S = V + ·

  • {#} · ((V ′)+ ∪ {¬} · (V ′)+ ∪ {∗})

∗ Protein properties

  • x: property x present (e.g. specific phosphate attached)
  • ¬x: property x absent (e.g. specific phosphate removed)
  • ∗: placeholder for arbitrary property setting

Examples

  • prot1#p# ∗ #¬p (subsumes activation states of prot1)
  • KaiC#¬KaiA#KaiB#4 (prot. complex, 4 ligands attached)

= ⇒ Application of reaction rules requires string matching

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

ΠCSM: System Components

Let S be the set of all multisets over S. ΠCSM = (V, V ′, R1, . . . , Rr, f1, . . . , fr, A, C, ∆τ) with Ri ∈ S × S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . is a reaction rule composed of two finite multisets fi : S − → N . . . . . . . . . . . . . . . . . . . .is a function corresponding to discrete kinetics of reaction Ri A ∈ S . . . . . . . . . . . . . . . . . . . is a multiset of axioms representing the initial molecular configuration C ∈ R+ spatial capacity of the module (vessel or compartment) ∆τ ∈ R+ . . . . . . . . . . . . . . . . . . . . . . . . . . . time discretisation interval

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

ΠCSM: Matching

Let S be a string-object syntax. Two string-objects match iff there is at least one common wild card-free representation: Match ⊆ S × S Match =

  • m∈N

{(p#p1#p2 . . . #pm, s#s1#s2 . . . #sm) | (p = s) ∧ ∀j ∈ {1, . . . , m} : [(pj = sj) ∨ (pj = ∗) ∨ (sj = ∗) ∨ ((pj = ¬q) ∧ (sj = q)) ∨ ((sj = ¬q) ∧ (pj = q))]}

  • Match is a symmetric relation
  • Requires minimal similarity between string-objects with

incomplete information

  • Uncertainty interpreted as arbitrary replacement by

available properties

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

ΠCSM: Matching

Let S be a string-object syntax. Two string-objects match iff there is at least one common wild card-free representation: Example

C#D#−p C#T#p C#T#−p C#*#p C#D#* C#*#* E#*#* V’ = {D, T, p} V = {C, E} C#D#p E#*#* C#*#* C#D#* C#*#p C#T#−p C#T#p C#D#−p C#D#p

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

ΠCSM: Dynamical System Behaviour (I)

  • Successive progression of

configuration Lt ∈ S over time t ∈ N starting from axioms A

  • ∆τ: span between t and t + 1
  • Conflict handling by prioritisation
  • f reaction rules

L0 = L0,0 = A Lt,1 = Lt,0 ⊖ Reactantst,1 ⊎ Productst,1 if Reactantst,1 ⊆ Lt,0 Lt,0 otherwise . . . Lt+1 = Lt,r = Lt,r−1 ⊖ Reactantst,r ⊎ Productst,r if Reactantst,r ⊆ Lt,r−1 Lt,r−1 otherwise

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

2 A + B ➜ C D A B B A A D A B B A A 2 A + B ➜ C 2 A + D ➜ E B C A D

?

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

ΠCSM: Dynamical System Behaviour (II)

Estimation of multisets Reactantst,j and Productst,j at time t concerning reaction Rj = (Aj, Bj) ∈ S × S denoted Aj(a1) a1 + . . . + Aj(ap) ap − → Bj(b1) b1 + . . . + Bj(bq) bq includes

  • Matching between string-objects in Lt and those in Aj
  • Consideration of stoichiometry captured by multisets Aj, Bj
  • Evaluation of kinetic law expressed by scalar function fj

Reactantst,j =

  • e1∈Match(a1)

. . .

  • ep∈Match(ap)

fj

  • {(e1, ∞), . . . , (ep, ∞)} ∩ Lt,j−1
  • ·
  • (e1, Aj(a1)), . . . , (ep, Aj(ap))
  • Productst,j =
  • e1∈Match(a1)

. . .

  • ep∈Match(ap)

fj

  • {(e1, ∞), . . . , (ep, ∞)} ∩ Lt,j−1
  • ·
  • (b1, Bj(b1)), . . . , (bq, Bj(bq))
  • Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics

Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

ΠCSM: Discrete Reaction Kinetics

Scalar function fj provides number of turns for application of reaction rule Rj. Rate constant: kj = ˆ kj · C · ∆τ (Euler). fj(Lt) =    kj

  • ∀α∈Match(Aj)∩Match(Lt) : (Rj=(Aj,Bj))

ˆ f(Lt(α))|Match(Aj)∩{(α,∞)}|     Selected kinetic laws ˆ f([Z])

Kinetics Activation Repression Mass-Action (no saturation) reactant conc.

  • reac. rate

v [Z] ˆ f([Z]) = [Z] − Michaelis-Menten (saturation) reactant conc.

  • reac. rate

v [Z] ˆ f([Z]) =

[Z] Θ+[Z]

reactant conc. [Z]

  • reac. rate

v ˆ f([Z]) = “ 1 −

[Z] Θ+[Z]

” Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Circadian Clocks

Characteristics

  • Self-sustained biochemical oscillators
  • Period of approx. 24 hours persisting under constant

environmental conditions (e.g. constant darkness)

  • Temperature compensation within physiological range
  • Capability of entrainment by external stimuli (e.g. light/dark
  • r temperature cycles)
  • Reaction system with at least one feedback loop

High scientific impact because . . .

  • Circadian clock as a potential universal property of life
  • Self-sustainability and high precision of bio-oscillators
  • Chronobiological control systems for manifold processes
  • Several independent evolutionary origins assumed

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Cyanobacterium Synechococcus elongatus

“Simplest cells known to exhibit circadian phenomena”

www.genome.jgi−psf.org www.wikipedia.org 1µm

Prokaryotic autotrophic picoplankton in tropical oceans Genome: 2.4 . . . 2.7 Mbp

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Components of Circadian Clock: Key Protein KaiC

  • Homohexamer (“double doughnut”) with 12 ATP molecules
  • Protein kinase (transferase), length: 519 residues

PDB Protein Data Bank, ID: 2gbl, www.rcsb.org/pdb

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Key Clock Proteins KaiA and KaiB

  • KaiA: protein binding molecular function reported,

length: 289 residues

  • KaiB: no further molecular function reported,

length: 108 residues

KaiA protein structure from PDB Protein Data Bank, ID: 1r8j www.rcsb.org/pdb KaiB protein structure from PDB Protein Data Bank, ID: 2qke Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

KaiABC Oscillator: Reaction Cycle

KaiA KaiA KaiA KaiA KaiA KaiB KaiB KaiB KaiB

P P P P PP P P P P P P P P P P P P P P

?

successive dephosphorylation successive phosphorylation

Incomplete information about interphase feedback loops

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

KaiC Oscillating Behaviour in Seven Phases

(A) PAGE gel and oscillation phases: U1, U2 (upward), P (peak), D1, D2, D3 (descent), T (trough) (B) Representative electron microscopic images of KaiC (C) and complexes KaiA•KaiC (AC), KaiB•KaiC (BC)

  • T. Mori, D.R. Williams, M.O. Byrne, X. Qin, M. Egli, H.S. Mchaourab, P

.L. Stewart, C.H. Johnson. Elucidating the Ticking of an In Vitro Circadian Clockwork. PLoS Biology 5(4):841–853, 2007, doi: 10.1371/journal.pbio.0050093 Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Relative Frequencies of KaiC and Complexes in Phases D1, D2, D3, T, U1, U2, P

(C) Assignment of frequency classes I KaiC hexamers alone, II KaiA•KaiC, III KaiB•KaiC, IV KaiA•KaiB•KaiC (D) Representative electron microscopic images of classes

  • T. Mori, D.R. Williams, M.O. Byrne, X. Qin, M. Egli, H.S. Mchaourab, P

.L. Stewart, C.H. Johnson. Elucidating the Ticking of an In Vitro Circadian Clockwork. PLoS Biology 5(4):841–853, 2007, doi: 10.1371/journal.pbio.0050093 Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

The Model ΠKaiABC at a Glance

ΠKaiABC = (V, V ′, R1, . . . , R17, f1, . . . , f17, A, C, ∆τ) V = {A, B, C}....................identifiers of proteins KaiA, KaiB, KaiC V ′ = {A, B} ∪ ................KaiA, KaiB within a complex associated to KaiC {0, 1, 2, 3, 4, 5, 6}.....number of attached phosphates R1 = C#¬A#B#0 + A − → C#A#¬B#1 + B R2 = C#A# ∗ #1 + A − → C#A# ∗ #2 + A R3 = C#A# ∗ #2 + A − → C#A# ∗ #3 + A R4 = C#A# ∗ #3 + A − → C#A# ∗ #4 + A R5 = C#A# ∗ #4 + A − → C#A# ∗ #5 + A R6 = C#A#¬B#5 + B − → C#¬A#B#6 + A R7 = C# ∗ #B#6 + B − → C# ∗ #B#5 + B R8 = C# ∗ #B#5 + B − → C# ∗ #B#4 + B R9 = C# ∗ #B#4 + B − → C# ∗ #B#3 + B R10 = C# ∗ #B#3 + B − → C# ∗ #B#2 + B R11 = C# ∗ #B#2 + B − → C# ∗ #B#1 + B R12 = C# ∗ #B#1 + B − → C# ∗ #B#0 + B R13 = C#¬A#B#∗ + A − → C#A#¬B#∗ + B R14 = C#A#¬B#∗ + B − → C#¬A#B#∗ + A R15 = A − → ∅ R16 = B − → ∅ R17 = C# ∗ # ∗ #∗ − → ∅ . . .

Discrete Michaelis-Menten kinetics

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Simulation Results: Individual KaiABC Subproducts

100 200 300 400 500 600 2 4 6 8 10 12 14 16 18 20 22 24 protein abundance time scale (hours) C-AB0 CA-B1 CA-B2 CA-B3 CA-B4 CA-B5 C-AB6 C-AB5 C-AB4 C-AB3 C-AB2 C-AB1

Temporal courses of 12 specific KaiABC subproducts representing the process status of the reaction cycle. Kinetic parameters and initial amounts adjusted in a way to obtain a period of ≈ 24 hours and symmetry among individual

  • scillations.

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Focussing on the Level of Phosphorylation

200 400 600 800 1000 1200 2 4 6 8 10 12 14 16 18 20 22 24 protein abundance time scale (hours) C**1 C**2 C**3 C**4 C**5 C**6 C**0

Temporal courses of KaiABC subproducts subsumed by their level of phosphorylation ranging from 0 to 6. Kinetic parameters and initial amounts adjusted in a way to obtain a period of ≈ 24 hours and symmetry among individual oscillations.

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Focussing on KaiABC Complex Formation

1500 2000 2500 3000 3500 2 4 6 8 10 12 14 16 18 20 22 24 protein abundance time scale (hours) CA** C*B*

Temporal courses of KaiABC subproducts separated into two groups by association of KaiA resp. KaiB to KaiC. Kinetic parameters and initial amounts adjusted in a way to obtain a period of ≈ 24 hours and symmetry among individual

  • scillations.

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Reaction Network Reconstruction from Scratch

?

  • Partially unknown topology
  • Some behavioural data available
  • Reconstruction of appropriate reaction network candidates
  • Capturing ideas and inspirations for network topologies

and parameterisation suitable for specific task

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Reaction Network Reconstruction: A Challenging Task

Exhaustive candidate enumeration

  • Exponential growth of search space:

n species − → 22n possible first-order reactions Finding homologies

  • Employ synergetic effects: known networks with similar

functionality could be adapted Bottom-up engineering

  • Provide small functional units and combine them towards

entire network (constructive approach) Learning strategies

  • Reduce a huge full network by successive weighting of

reactions along with available behavioural data Artificial network evolution

  • Universal heuristics adopted from biological evolution

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Reaction Network Reconstruction: A Challenging Task

Exhaustive candidate enumeration

  • Exponential growth of search space:

n species − → 22n possible first-order reactions Finding homologies

  • Employ synergetic effects: known networks with similar

functionality could be adapted Bottom-up engineering

  • Provide small functional units and combine them towards

entire network (constructive approach) Learning strategies

  • Reduce a huge full network by successive weighting of

reactions along with available behavioural data Artificial network evolution

  • Universal heuristics adopted from biological evolution

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Reaction Network Reconstruction: A Challenging Task

Exhaustive candidate enumeration

  • Exponential growth of search space:

n species − → 22n possible first-order reactions Finding homologies

  • Employ synergetic effects: known networks with similar

functionality could be adapted Bottom-up engineering

  • Provide small functional units and combine them towards

entire network (constructive approach) Learning strategies

  • Reduce a huge full network by successive weighting of

reactions along with available behavioural data Artificial network evolution

  • Universal heuristics adopted from biological evolution

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Reaction Network Reconstruction: A Challenging Task

Exhaustive candidate enumeration

  • Exponential growth of search space:

n species − → 22n possible first-order reactions Finding homologies

  • Employ synergetic effects: known networks with similar

functionality could be adapted Bottom-up engineering

  • Provide small functional units and combine them towards

entire network (constructive approach) Learning strategies

  • Reduce a huge full network by successive weighting of

reactions along with available behavioural data Artificial network evolution

  • Universal heuristics adopted from biological evolution

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Reaction Network Reconstruction: A Challenging Task

Exhaustive candidate enumeration

  • Exponential growth of search space:

n species − → 22n possible first-order reactions Finding homologies

  • Employ synergetic effects: known networks with similar

functionality could be adapted Bottom-up engineering

  • Provide small functional units and combine them towards

entire network (constructive approach) Learning strategies

  • Reduce a huge full network by successive weighting of

reactions along with available behavioural data Artificial network evolution

  • Universal heuristics adopted from biological evolution

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Why Artificial Evolution for Network Reverse Engineering

  • Systems Biology deals with interplay of

biological components rather than components themselves.

  • Accumulation of small modifications in

component’s interplay can result in a new quality of the entire network. = ⇒ Artificial evolution can explore network structure.

  • Help in understanding emergence of biological complexity.

= ⇒ Evolution becomes observable.

  • Furthermore, bio-inspired approaches provide a flexible,

fault-tolerant, reliable paradigm. = ⇒ Artificial evolution can find unexpected, unconventional solutions.

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze www.wordpress.com

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Why Artificial Evolution for Network Reverse Engineering

  • Systems Biology deals with interplay of

biological components rather than components themselves.

  • Accumulation of small modifications in

component’s interplay can result in a new quality of the entire network. = ⇒ Artificial evolution can explore network structure.

  • Help in understanding emergence of biological complexity.

= ⇒ Evolution becomes observable.

  • Furthermore, bio-inspired approaches provide a flexible,

fault-tolerant, reliable paradigm. = ⇒ Artificial evolution can find unexpected, unconventional solutions.

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze www.wordpress.com

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Why Artificial Evolution for Network Reverse Engineering

  • Systems Biology deals with interplay of

biological components rather than components themselves.

  • Accumulation of small modifications in

component’s interplay can result in a new quality of the entire network. = ⇒ Artificial evolution can explore network structure.

  • Help in understanding emergence of biological complexity.

= ⇒ Evolution becomes observable.

  • Furthermore, bio-inspired approaches provide a flexible,

fault-tolerant, reliable paradigm. = ⇒ Artificial evolution can find unexpected, unconventional solutions.

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze www.wordpress.com

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Why Artificial Evolution for Network Reverse Engineering

  • Systems Biology deals with interplay of

biological components rather than components themselves.

  • Accumulation of small modifications in

component’s interplay can result in a new quality of the entire network. = ⇒ Artificial evolution can explore network structure.

  • Help in understanding emergence of biological complexity.

= ⇒ Evolution becomes observable.

  • Furthermore, bio-inspired approaches provide a flexible,

fault-tolerant, reliable paradigm. = ⇒ Artificial evolution can find unexpected, unconventional solutions.

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze www.wordpress.com

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Evolutionary Computing

  • Abstraction and formalisation of evolutionary processes
  • Individuals (genotype, phenotype) and population
  • Evolutionary operators along with fitness evaluation
  • Heuristical optimisation technique, experimentally driven

Artificial evolution

  • Initiated by Friedmann 1956
  • Pioneers: Rechenberg, Schwefel, Fogel, Holland, Banzhaf,

Koza, Sauro, . . .

pics.goingon.com Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Facets and Specialties

Evolutionary Programming

Evolutionary Computing

Genetic Algorithms Genetic Programming Evolution Strategies Evolutionary Algorithms phenotype−based genotype−based

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Facets and Specialties

Evolutionary Programming

Evolutionary Computing

Genetic Algorithms Genetic Programming Evolution Strategies Evolutionary Algorithms phenotype−based genotype−based

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Central Loop in Evolutionary Algorithms

1. 2. 3. 4. 5. 6. 7. 8. fitness evaluation initialize population recombination selection of mating partners termination test environmental selection mutation fitness evaluation

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

SBMLevolver: Two-Level Evolutionary Algorithm

  • Separation of structural evolution from parameter fitting
  • Idea: parameters can adapt to mutated network structure

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mutate parameters create offspring & selection parameter sets

Parameter Fitting & Fitness Evaluation Selection & Offspring Creation Population

  • Upper level: network structure
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= ⇒ open-source freeware: http://users.minet.uni-jena.de/∼biosys/esignet

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Structural Evolution

1. 2. 3. 4. 5. 7. 6. 8. fitness evaluation initialize population recombination return population parameter fitting mutation hand over to parameter fitting selection of mating partners

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

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Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Initialization of Network Population

Initial population configurable, typically 50 . . . 100 network individuals as SBML files Empty

  • Network reconstruction from scratch

Randomly choosen

  • Individual networks randomly chosen, upper/lower limits for

numbers of species, reactions, and kinetic parameter values Taken from imported SBML file

  • Generate a number of file copies
  • Dedicated species, reactions, and kinetic parameters can

be marked as fixed during evolution

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-40
SLIDE 40

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Initialization of Network Population

Initial population configurable, typically 50 . . . 100 network individuals as SBML files Empty

  • Network reconstruction from scratch

Randomly choosen

  • Individual networks randomly chosen, upper/lower limits for

numbers of species, reactions, and kinetic parameter values Taken from imported SBML file

  • Generate a number of file copies
  • Dedicated species, reactions, and kinetic parameters can

be marked as fixed during evolution

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-41
SLIDE 41

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Initialization of Network Population

Initial population configurable, typically 50 . . . 100 network individuals as SBML files Empty

  • Network reconstruction from scratch

Randomly choosen

  • Individual networks randomly chosen, upper/lower limits for

numbers of species, reactions, and kinetic parameter values Taken from imported SBML file

  • Generate a number of file copies
  • Dedicated species, reactions, and kinetic parameters can

be marked as fixed during evolution

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-42
SLIDE 42

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Fitness Evaluation

Specification of dynamical behaviour

  • Input/output table: desired course
  • f input and output species

at discrete points in time

  • Distinction between finite number of

cases (runs) in input/output table

  • Penalties can be set

Fitness evaluation

  • Numerical integration of reaction

network using ODE solver (SOSlib)

  • Currently, mass-action kinetics
  • Fitness measure given by weighted

squared distance to target time course (output species)

  • Minimisation of fitness value (!)

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-43
SLIDE 43

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Fitness Evaluation

Specification of dynamical behaviour

  • Input/output table: desired course
  • f input and output species

at discrete points in time

  • Distinction between finite number of

cases (runs) in input/output table

  • Penalties can be set

Fitness evaluation

  • Numerical integration of reaction

network using ODE solver (SOSlib)

  • Currently, mass-action kinetics
  • Fitness measure given by weighted

squared distance to target time course (output species)

  • Minimisation of fitness value (!)

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

addition of two positive real numbers (introductory example) fitness development (best, average, worst)

slide-44
SLIDE 44

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Mutation Operators

Seven mutations available, randomly selected

  • Addition/deletion of a species
  • Addition/deletion of a reaction
  • Connection/removal of existing

species to/from a reaction

  • Duplication of a species with

all its reactions Network size can be limited. = ⇒ One or several mutations per turn

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

addition of a species deletion of a species addition of a reaction deletion of a reaction disconnection of species connection of species species duplication

slide-45
SLIDE 45

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Parameter Fitting

  • Adaptation of networks after structural mutation(s)
  • Separate evolutionary algorithm
  • Generate copies of networks

resulted from structural mutation(s)

  • Random selection of one or

several kinetic parameters

  • Mutation: addition of

Gauss variable

  • Plausibility check
  • No recombination
  • Environmental selection

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

Ν(0,σ) parameter increment / decrement probability

slide-46
SLIDE 46

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Environmental Selection

Small population size

  • Due to high computational costs of fitness evaluation

Self-adaptation of strategy parameters (Gaussian distribution)

  • Balancing between exploration of search space and

fine-tuning Non-overlapping generations

  • Comma-selection supports self adaptation

Parameter settings copied from parent to offspring

  • Incremental parameter fitting

Fitness proportional selection

  • Combines survival of the fittest with ability to leave local
  • ptima and keeps diversity of population

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-47
SLIDE 47

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Environmental Selection

Small population size

  • Due to high computational costs of fitness evaluation

Self-adaptation of strategy parameters (Gaussian distribution)

  • Balancing between exploration of search space and

fine-tuning Non-overlapping generations

  • Comma-selection supports self adaptation

Parameter settings copied from parent to offspring

  • Incremental parameter fitting

Fitness proportional selection

  • Combines survival of the fittest with ability to leave local
  • ptima and keeps diversity of population

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-48
SLIDE 48

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Environmental Selection

Small population size

  • Due to high computational costs of fitness evaluation

Self-adaptation of strategy parameters (Gaussian distribution)

  • Balancing between exploration of search space and

fine-tuning Non-overlapping generations

  • Comma-selection supports self adaptation

Parameter settings copied from parent to offspring

  • Incremental parameter fitting

Fitness proportional selection

  • Combines survival of the fittest with ability to leave local
  • ptima and keeps diversity of population

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-49
SLIDE 49

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Environmental Selection

Small population size

  • Due to high computational costs of fitness evaluation

Self-adaptation of strategy parameters (Gaussian distribution)

  • Balancing between exploration of search space and

fine-tuning Non-overlapping generations

  • Comma-selection supports self adaptation

Parameter settings copied from parent to offspring

  • Incremental parameter fitting

Fitness proportional selection

  • Combines survival of the fittest with ability to leave local
  • ptima and keeps diversity of population

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-50
SLIDE 50

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Environmental Selection

Small population size

  • Due to high computational costs of fitness evaluation

Self-adaptation of strategy parameters (Gaussian distribution)

  • Balancing between exploration of search space and

fine-tuning Non-overlapping generations

  • Comma-selection supports self adaptation

Parameter settings copied from parent to offspring

  • Incremental parameter fitting

Fitness proportional selection

  • Combines survival of the fittest with ability to leave local
  • ptima and keeps diversity of population

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-51
SLIDE 51

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Termination and Final Network Simplification

Termination

  • Best fitness below configurable threshold (ideally = 0)
  • After configurable number of generations
  • After configurable number of fitness evaluations

Final network simplification

  • Optional, only deletion of species keeping minimal fitness

Challenges and insufficiencies

  • Premature convergence along with low diversity of

population

  • Overfitting (perfect replication of test cases but no further

functionality of network)

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-52
SLIDE 52

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Termination and Final Network Simplification

Termination

  • Best fitness below configurable threshold (ideally = 0)
  • After configurable number of generations
  • After configurable number of fitness evaluations

Final network simplification

  • Optional, only deletion of species keeping minimal fitness

Challenges and insufficiencies

  • Premature convergence along with low diversity of

population

  • Overfitting (perfect replication of test cases but no further

functionality of network)

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-53
SLIDE 53

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Termination and Final Network Simplification

Termination

  • Best fitness below configurable threshold (ideally = 0)
  • After configurable number of generations
  • After configurable number of fitness evaluations

Final network simplification

  • Optional, only deletion of species keeping minimal fitness

Challenges and insufficiencies

  • Premature convergence along with low diversity of

population

  • Overfitting (perfect replication of test cases but no further

functionality of network)

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-54
SLIDE 54

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Third Root Network

initial conc. of input species → steady state conc. of output species

  • T. Lenser, T. Hinze, B. Ibrahim, P

. Dittrich. Towards Evolutionary Network Reconstruction Tools for Systems Biology. In E. Marchiori, J.H. Moore, J.C. Rajapakse (Eds.), Proceedings Fifth European Conference on Evolutionary Computation, Machine Learning and Data Mining in Bioinformatics, Springer LNCS 4447:132-142, 2007 Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-55
SLIDE 55

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Addition

dx1 dt = 0 dx2 dt = 0 dy dt = k1x1 + k2x2 − k3y Let k1 = k2 = k3 > 0. Steady state: y = lim

t→∞

  • 1 − e−k1t

· (x1 + x2) = x1 + x2

  • B. Schau, T. Hinze, T. Lenser, I. Heiland, S. Schuster. Control System-Based Reverse Engineering of Circadian
  • Oscillators. In I. Grosse, S. Neumann, S. Posch, F. Schreiber, P

. Stadler (Eds.), Proceedings German Conference on Bioinformatics (GCB2009), p. 126-127, Martin-Luther University Halle-Wittenberg, 2009 Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-56
SLIDE 56

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Non-Negative Subtraction

dx1 dt

=

dx2 dt

=

dy dt

= −k2yz − k1y + k1x1

dz dt

= k1x2 − k2yz Let k1 > 0 and k2 > 0. Steady state: y = x1 − x2 iff x1 > x2 0 otherwise

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-57
SLIDE 57

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Multiplication

dx1 dt = 0 dx2 dt = 0 dy dt = k1x1x2 − k2y Let k1 = k2 > 0. Steady state: y = lim

t→∞

  • 1 − e−k1t

· x1 · x2 = x1 · x2

  • B. Schau, T. Hinze, T. Lenser, I. Heiland, S. Schuster. Control System-Based Reverse Engineering of Circadian
  • Oscillators. In I. Grosse, S. Neumann, S. Posch, F. Schreiber, P

. Stadler (Eds.), Proceedings German Conference on Bioinformatics (GCB2009), p. 126-127, Martin-Luther University Halle-Wittenberg, 2009 Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-58
SLIDE 58

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Division

dx1 dt = 0 dx2 dt = 0 dy dt = k2x2 − k1x1y Let k1 = k2 > 0. Steady state: y = lim

t→∞

  • 1 − e−k1t

· x2

x1 iff x1 > 0

lim

t→∞

  • k2x2dt otherwise

=   

x2 x1

iff x1 > 0 → ∞ iff x1 = 0 and x2 > 0 iff x1 = 0 and x2 = 0

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-59
SLIDE 59

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Generalised Circadian System as Control System

Separation of the system into smaller functional components

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-60
SLIDE 60

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Circadian Entrainment as Phase Locking Loop

plant and sensor controller actuator basis oscillator time moving average element (low pass filter) time difference element time plant input affects frequency accumulated signal difference signal activation inhibition reference value (external light/dark rhythms)

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-61
SLIDE 61

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Benefit from Symbiosis

membrane systems + variable molecular structures + discretised reaction kinetics . . . . . . . . . . . . . . . . in systems biology. Membrane systems approach ΠCSM

  • String-objects denoted by regular expressions can manage

descriptional complexity of protein binding states

  • Coping with incomplete information by superpositioning of

molecular configurations

  • Discretised reaction kinetics enables representation of

structural dynamics Artificial reaction network evolution

  • Promising heuristic approach for network reconstruction
  • Exploring structural variability
  • Applicable for small modules (≤ 15 species), extendable

by hierarchical evolution = ⇒ Outlook: artificial evolution of membrane systems

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-62
SLIDE 62

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Benefit from Symbiosis

membrane systems + variable molecular structures + discretised reaction kinetics . . . . . . . . . . . . . . . . in systems biology. Membrane systems approach ΠCSM

  • String-objects denoted by regular expressions can manage

descriptional complexity of protein binding states

  • Coping with incomplete information by superpositioning of

molecular configurations

  • Discretised reaction kinetics enables representation of

structural dynamics Artificial reaction network evolution

  • Promising heuristic approach for network reconstruction
  • Exploring structural variability
  • Applicable for small modules (≤ 15 species), extendable

by hierarchical evolution = ⇒ Outlook: artificial evolution of membrane systems

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-63
SLIDE 63

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Benefit from Symbiosis

membrane systems + variable molecular structures + discretised reaction kinetics . . . . . . . . . . . . . . . . in systems biology. Membrane systems approach ΠCSM

  • String-objects denoted by regular expressions can manage

descriptional complexity of protein binding states

  • Coping with incomplete information by superpositioning of

molecular configurations

  • Discretised reaction kinetics enables representation of

structural dynamics Artificial reaction network evolution

  • Promising heuristic approach for network reconstruction
  • Exploring structural variability
  • Applicable for small modules (≤ 15 species), extendable

by hierarchical evolution = ⇒ Outlook: artificial evolution of membrane systems

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-64
SLIDE 64

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Benefit from Symbiosis

membrane systems + variable molecular structures + discretised reaction kinetics . . . . . . . . . . . . . . . . in systems biology. Membrane systems approach ΠCSM

  • String-objects denoted by regular expressions can manage

descriptional complexity of protein binding states

  • Coping with incomplete information by superpositioning of

molecular configurations

  • Discretised reaction kinetics enables representation of

structural dynamics Artificial reaction network evolution

  • Promising heuristic approach for network reconstruction
  • Exploring structural variability
  • Applicable for small modules (≤ 15 species), extendable

by hierarchical evolution = ⇒ Outlook: artificial evolution of membrane systems

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-65
SLIDE 65

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Eleventh International Conference on Membrane Computing (CMC11)

24-27 August 2010, Jena, Germany

Eleventh International Conference on Membrane Computing

http://cmc11.uni-jena.de

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze

slide-66
SLIDE 66

Motivation CSM ΠCSM KaiABC Oscillator ΠKaiABC Artificial Evolution SBMLevolver Evolved Networks CMC11

Special Thanks go to . . .

Jena Centre for Bioinformatics (JCB)

... you for your attention. Questions? ... my CMC11 coworkers Thorsten Lenser

Bio Systems Analysis Group, FSU Jena Bio Systems Analysis Group, FSU Jena

Gabi Escuela Jörn Behre

Department of Bioinformatics, FSU Jena

... the hosting organizations

Friedrich Schiller University of Jena (FSU)

Rudolf Freund

Vienna University of Technology

Membrane Systems + Variable Molecular Structures + Discretised Reaction Kinetics Thomas Hinze