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Chemical Organization Theory How are living systems organized? How do they evolve? Peter Dittrich Bio Systems Analysis Group FSU Jena Friedrich-Schiller-Universität Jena Jena Centre for Bioinformatics

Bio Systems Analysis Group Use computational approaches to explain complex dynamical phenomena found in living systems ESIGNET Evolving Cell Signalling Networks in silico (T. Hinze, T. Lenser, EU) Systems Analysis of the Cell Cycle (B. Ibrahim, DAAD) Chemical Network Theory and Simulation (P. Speroni d.f., F. Cenler, BMBF) Organic Computing: Chemical Prgramming (N. Matsumaru, DFG) Semantics of Biological Models (Ch. Knüpfer, RLS) Autonomous Experimentation (N. Matsumaru, BMBF) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 2

How is life (and its origin) organized? 1. What is the bio-chemical organization of an organism? 2. How did the bio-chemical organization of the pre-prebiotic soup evolved? 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 3

Quality (not quantity)

Q1 How does the lattice of organizations of an organism looks like? lattice of organizations = organizational structure 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 5

What is an answer? [Source: Puchalka/Kierzek (2004)Biophys. J. 86, 1357] 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 6

Reaction Systems

Example Level IV: Catalytic Flow System 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 8

Example Level IV: Catalytic Flow System + + (catalytic) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 9

Example Level IV: Catalytic Flow System + + (catalytic) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 10

Example Level IV: Catalytic Flow System + + (catalytic) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 11

Example Level IV: Catalytic Flow System + + k 1 k 2 (catalytic) dx 1 /dt = k 2 x 2 x 2 dx 2 /dt = k 1 x 1 x 2 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 12

Example Level IV: Catalytic Flow System + + k 1 k 2 (catalytic) reaction network dilution flux dx 1 /dt = k 2 x 2 x 2 - x 1 dx 2 /dt = k 1 x 1 x 2 x 2 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 13

Chemical Organization Theory

Chemical Organization Organization := a set of molecules that is (algebraically) closed and self-maintaining There is no reaction producing any other molecules than the member of the set. Within the set, all molecules consumed by a reaction can be reproduced by a reaction. [Speroni di Fenizio/Dittrich (2005/7) inspired by Fontana, Buss, Rössler, Eigen, Kauffman, Maturana, Varela, Uribe] 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 15

Fixed Point and Organization Theorem Given a fixed point of the ODE describing the dynamics of a reaction system, then the set of molecules represented by that fixed point is an organization. [Dittrich/Speroni di Fenizio, (2005,2007)] 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 16

Practical View 4 4 Chemical 1 Organization 1 Theory 2 3 2 3 Reaction network Organization 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 17

All Organizations Organization 4 4 Chemical 1 Organization 1 Theory 2 3 2 3 Reaction network Organizations 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 18

Lattice of Organizations Hasse diagram of the organizations 4 {1,2,3,4} 2 1 3 Chemical Organization Theory {1} {2, 3} { } Reaction network Organizations 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 19

Generate Organization Hasse diagram of the organizations 4 {1,2,3,4} 2 1 3 Chemical Organization Theory {1} {2, 3} { } Reaction network G O ({3, 4}) =? Organizations 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 20

Generate Organization Hasse diagram of the organizations 4 {1,2,3,4} 2 1 3 Chemical Organization Theory {1} {2, 3} Reaction network generate organization G Org ({3, 4}) = {1} { } Organizations 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 21

Union of Organizations Hasse diagram of the organizations 4 {1,2,3,4} 1 Chemical Organization Theory {1} {2, 3} 2 3 Reaction network generate organization G Org ({3, 4}) = {1} {1} U O {2, 3} := G Org ({1} U {2,3}) union of organizations 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 22 { } Organizations

Self-maintenance Organization := closed & self-maintaining set of (molecular) species 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 23

Example 1 a + b -> 2 b 2 b a + c -> 2 c b -> d a d e c -> d b + c -> e 2 c -> a a -> b -> c -> d -> e -> 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 24

Example 1 Organization {a, b, d} 2 b a d e 2 c 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 25

Example 1 Organization {a, b, d} 2 b a d e 2 c 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 26

Example 1 Organization {a, b, d} 2 b 1. Find flux vector outside of org. = 0 a d 0 e 0 0 0 2 c 0 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 27

Example 1 1 Organization {a, b, d} 2 b 9 8 1. Find flux vector 10 a 1 d 1 0 e 0 outside of org. = 0 inside of org. > 0 0 0 2 c 0 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 28

Example 1 1 Organization {a, b, d} 2 b 9 8 1. Find flux vector 10 a 1 d 1 0 e 0 0 outside of org. = 0 inside of org. > 0 0 0 2 c 0 0 2. Check production rates outside of org. = 0 (closure) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 29

Example 1 1 0 Organization {a, b, d} 2 b 10 0 a 1 9 8 7 d 1 0 e 1. Find flux vector outside of org. = 0 0 inside of org. > 0 0 0 0 2 c 0 0 2. Check production rates outside of org. = 0 (closure) inside of org. 0 (self-maint.) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 30

Example 1 All Organizationen 2 b a d e 2 c 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 31

Example 1 All Organizationen 2 b a d e 2 c a 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 32

Example 1 All Organizationen 2 b a d e 2 c a b d a 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 33

Example 1 All Organizationen 2 b a d e 2 c a b d a c d a 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 34

Example 1 2 b Hasse diagram of organizations a b c d e a d e 2 c a b d a c d a 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 35

Überlappende Hierarchie 2 b Hasse diagram of organizations a b c d e a d e 2 c a b d a c d a 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 36

Theorem: Fixed points are instances of organizations differential equation x&= 0 = f f (x) fixed point / (stationary solution) ( x 0 ) [ a] [ b] x = [ c] [ d] [ e] 0 x 4 7 = 0 11 0 { a, b, d } a b d Hasse diagram of organizations a b c d e a c d 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 37 a Dittrich/Speroni d.f., Bull. Math. Biol., 2007

Q1 How does the lattice of organizations of an organism looks like? organizational structure = lattice of organizations 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 38

Trivially, all organisms have at least one organization S O 2 W S + O 2O + W S O W {S, O, W} {S} 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 39

Is there more? S + O 1 2O 1 + W S + O 2 2O 2 + W S O W 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 40

Is there more? S + O 1 2O 1 + W S + O 1 + O 2 2O 2 + W S O W 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 41

How does the lattice organizations in an organism looks like? number? hight? size distribution? 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 42

We looked at a couple of network models of real systems photochemistries (dead, closed but not isolated systems) metabolism regulated metabolism lambda-phage HIV - immunesystem 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 43

Population Dynamics HIV Immunesystem Model

initial state Test-bed:HIV Virus Dynamics uninfected CD4+ T cells infected CD4+ T cells CTL precursors CTL effectors x& = λ y& = w& = z& = simulation model of HIV replication (4 ODEs) dx βxy cxyw cqyw [Wodarz/Nowak, PNAS 96:14464,1999] βxy ay cqyw bw state after some time hz uninfected CD4+ T cells infected CD4+ T cells CTL precursors CTL effectors pyz CTL = cytotoxic T lymphocytes 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 45

HIV Dynamics: Mathematical analysis 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 46

HIV Immunsystem Populationsmodell T-Zelle infizierte T-Zelle CTL-Pre CTL-Ef Modell nach: C.D. Wodarz, M. A. Nowak, PNAS 96 (1999), 14464-13369 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 47

HIV Immunsystem Populationsmodell T-Zelle + infizierte-t-zelle 2 infizierte-t-zelle T-Zelle 2 infizierte T-Zelle CTL-Pre CTL-Ef Modell nach: C.D. Wodarz, M. A. Nowak, PNAS 96 (1999), 14464-13369 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 48

HIV Immunsystem Populationsmodell T-Zelle + infizierte T-Zelle + CTL-Pre T-Zelle + infizierte T-Zelle + 2 CTL-Pre T-Zelle infizierte T-Zelle 2 CTL-Pre CTL-Ef Modell nach: C.D. Wodarz, M. A. Nowak, PNAS 96 (1999), 14464-13369 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 49

HIV Immunsystem Populationsmodell T-Zelle 2 infizierte T-Zelle 2 CTL-Pre CTL-Ef Modell nach: C.D. Wodarz, M. A. Nowak, PNAS 96 (1999), 14464-13369 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 52

Organisation := abgeschlossen und selbsterhaltend T-Zelle 2 infizierte T-Zelle 2 CTL-Pre CTL-Ef Organisation := := (algebraisch) abgeschlossene und und selbsterhaltende Molekülmenge P. Dittrich, P. Speroni di Fenizio, Chemical organization theory, Bull. Math. Biol. (2007), in print N. Matsumaru, P. Speroni di Fenizio, F. Centler, P. Dittrich (2005), A Case Study of Chemical Organization Theory Applied to Virus Dynamics. In: J. T. Kim (Ed.), Systems Biology Workshop at ECAL, Kent, (2005) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 53

Alle Organisationen T-Zelle 2 infizierte T-Zelle 2 CTL-Pre CTL-Ef P. Dittrich, P. Speroni di Fenizio, Chemical organization theory, Bull. Math. Biol. (2007), in print N. Matsumaru, P. Speroni di Fenizio, F. Centler, P. Dittrich (2005), A Case Study of Chemical Organization Theory Applied to Virus Dynamics. In: J. T. Kim (Ed.), Systems Biology Workshop at ECAL, Kent, (2005) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 54

Organisationshierachie Organisationshierachie T-Zelle 2 infizierte T-Zelle { T-Zelle, infizierte T-Zelle, CTL-Pre, CTL-Ef } 2 { T-Zelle, infizierte T-Zelle } CTL-Pre CTL-Ef { T-Zelle } P. Dittrich, P. Speroni di Fenizio, Chemical organization theory, Bull. Math. Biol. (2007), in print N. Matsumaru, P. Speroni di Fenizio, F. Centler, P. Dittrich (2005), A Case Study of Chemical Organization Theory Applied to Virus Dynamics. In: J. T. Kim (Ed.), Systems Biology Workshop at ECAL, Kent, (2005) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 55

Dynamics Organisationshierarchie ill { T-Zelle, infizierte T-Zelle, CTL-Pre, CTL-Ef } healthy { T-Zelle, infizierte T-Zelle } Zeit (d) ill { T-Zelle } P. Dittrich, P. Speroni di Fenizio, Chemical organization theory, Bull. Math. Biol. (2007), in print N. Matsumaru, P. Speroni di Fenizio, F. Centler, P. Dittrich (2005), A Case Study of Chemical Organization Theory Applied to Virus Dynamics. In: J. T. Kim (Ed.), Systems Biology Workshop at ECAL, Kent, (2005) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 56

Explain medication strategy Organisationsstruktur Medication strategy gesund krank { T-Zelle, infizierte T-Zelle, CTL-Pre, CTL-Ef } { T-Zelle, infizierte T-Zelle } gesund { T-Zelle } N. Matsumaru, P. Speroni di Fenizio, F. Centler, P. Dittrich (2005), A Case Study of Chemical Organization Theory Applied to Virus Dynamics. In: J. T. Kim (Ed.), Systems Biology Workshop at ECAL, Kent, (2005) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 57

Compare models N. Matsumaru, F. Centler, P. Speroni di Fenizio, P. Dittrich (2006); it - Information Technology, 48(3):1-9, 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 58

Evaluate model quality Organisationsstruktur gesund { T-Zelle, infizierte T-Zelle, CTL-Pre, CTL-Ef } Model quality krank { T-Zelle, infizierte T-Zelle } gesund { T-Zelle } N. Matsumaru, P. Speroni di Fenizio, F. Centler, P. Dittrich (2005), A Case Study of Chemical Organization Theory Applied to Virus Dynamics. In: J. T. Kim (Ed.), Systems Biology Workshop at ECAL, Kent, (2005) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 59

Application of Organization Theory to Planetary Photochemistries Mars 31 molecular species, 103 reactions main component: CO 2 (95%) http://www.fpsoftlab.com/images/screenshots/mars-640x480-1.jpg Y. L. Yung and W. B. DeMore (1999) Photochemistry of Planetary Atmospheres,Oxford University Press 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 60

Mars - Reaction Network File... 1 CO2 1 hv -> 1 CO 1 O 2 O -> 1 O2 1 O 1 O2 1 N2 -> 1 O3 1 N2 1 O 1 O2 1 CO2 -> 1 O3 1 CO2 1 O 1 O3 -> 2 O2 1 O 1 CO -> 1 CO2 1 O(1D) 1 O2 -> 1 O 1 O2 1 O(1D) 1 O3 -> 2 O2 1 O(1D) 1 O3 -> 1 O2 2 O 1 O(1D) 1 H2 -> 1 H 1 OH 1 O(1D) 1 CO2 -> 1 O 1 CO2 1 O(1D) 1 H2O -> 2 OH 2 H -> 1 H2 1 H 1 O2 -> 1 HO2 1 H 1 O3 -> 1 OH 1 O2 1 H 1 HO2 -> 2 OH 1 H 1 HO2 -> 1 H2 1 O2 1 H 1 HO2 -> 1 H2O 1 O 1 O 1 H2 -> 1 OH 1 H 1 O 1 OH -> 1 O2 1 H... 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 61

Mars at Night 13 molecules 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 62

Mars at Daytime 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 63

Distribution of Organizations 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 64

Randomizing the Network at daytime 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 65

How does the lattice of organizations of an organism looks like?? 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 66

Metabolic Models network from Palsson et al (?) analysis by C. Kaleta 2006 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 67

E. Coli Metabolism Model 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 68

E. coli Model (III) synthesis of some dntps lipid synthesis ACP or hmrsacp pyrimidine nucleotide synthesis q8 (quinone) central metabolism+ Minimal growth scenario: D-Glucose, O 2, Fe 2, NH 4, H +, Pi, SO 4 analysis by C. Kaleta, F. Centler, 2006 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 69

E. coli Model (II) Regulated Network Palsson/Covert Organization theory is able to predict growth phenotypes of various mutants quite nicely But the organizational structure is simple {S, O, W} C. Kaleta, F. Centler, P. Speroni di Fenizio, P. Dittrich (2007), submitted 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 70

Chemical Evolution Overview Organizations in Space Chemical Information Processing and Chemical Programming 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 71

Q2 How did the bio-chemical organization of the pre-prebiotic soup evolved? What is the characteristics of the organizational evolution? upward? downward?... 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 72

A View of Chemical Evolution 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 73

Actual Evolution 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 74

Actual Evolution 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 75

Actual Evolution vs. Organizational Evolution

Organizational Evolution 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 77

Organizational Evolution 1. Upwards [t1 t2] O O t1 t 2 Hasse diagram of organizations {1,2,3,4} {2, 3} {1} t1 t2 { } [2] [3] Organizations [1] [4] Dynamics 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 78

Organizational Evolution 1. Upwards [t1 t2] 2. Downwards [t2 t3] O O O t1 t 2 O t 2 t3 Hasse diagram of organizations {1,2,3,4} {2, 3} {1} t1 t2 t3 { } [2] [3] Organizations [1] [4] Dynamics 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 79

Organizational Evolution 1. Upwards [t1 t2] 2. Downwards [t2 t3] 3. Sidewards [t1 t3] O O O t1 t 2 O t 2 t3 otherwise Hasse diagram of organizations {1} {1,2,3,4} {2, 3} A set of existing species and an organization are not equivalent. e.g., {2,3,4} t1 t2 t3 [1] [4] Dynamics [2] [3] { } Organizations 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 80

Theoretical vs. Practical Theoretically: Every possible species is known. Entire reaction network is given. Every possible organization can be calculated. It is possible to define the dynamics on the ODE Practically: NOT every possible species is known. the entire network is NOT given. NOT evey possible organization can be calculated. 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 81

Perspective Change Hasse diagram of the organizations {1,2,3,4} {2, 3} {1} t1 t2 t3 { } [2] [3] Organizations [1] [4] Dynamics 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 82

Perspective Change {1,2,3,4} {1,2,3,4} {2, 3} {2, 3} {1} {1} {1} { } { } t1 t2 t3 { } [2] [3] [1] [4] Dynamics 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 83

Downward movement 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 84

Upward Movements (adding mutations) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 85

Q2 - Notes There are two levels of chemical evolution. Actual evolution (the actual vessel) Organizational evolution (upward, downward, sideward movements) These levels are different. If the organizations are complex, a downward movement (organizational level) can lead to a state with a higher diversity (actual evolution). 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 87

Space Space plays a fundamental role in many natural bio-chemical processes

Organizations in Space 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 89

Membranes Clusters Waves Spatial Scales Aspects of Space 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 90

Space [P. Speroni di Fenizi, P. Dittrich, Chemical Organizations at Different Spatial Scales, LNCS, Springer, 2007] 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 91

Chemical Computing Chemical Programming

10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 93 Chemical Flip-Flop Reaction network c D A C d A C D a C d a + + + + d C B D c B D C b D c b + + + + 0 0 0 0 + + + + D d C c B b A a D } B,c,C, d, A,b, a, M = { 256 possible sets of molecular species

Chemical Flip-Flop (with two inputs) 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 94

Flip-Flop dynamics 10.01.2008 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 95

Acknowledgements Pietro Speroni di Fenizio, Naoki Matsumaru, Florian Centler, Christoph Kaleta Friedrich-Schiller-Universität Jena Jena Centre for Bioinformatics BMBF (Federal Ministry of Education and Research, Germany) 0312704A, DFG (German Research Foundation) Grant Di 852/4-1