Chemical Organization Theory
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1 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
2 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) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 2
3 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? Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 3
4 Quality (not quantity)
5 Q1 How does the lattice of organizations of an organism looks like? lattice of organizations = organizational structure Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 5
6 What is an answer? [Source: Puchalka/Kierzek (2004)Biophys. J. 86, 1357] Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 6
7 Reaction Systems
8 Example Level IV: Catalytic Flow System Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 8
9 Example Level IV: Catalytic Flow System + + (catalytic) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 9
10 Example Level IV: Catalytic Flow System + + (catalytic) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 10
11 Example Level IV: Catalytic Flow System + + (catalytic) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 11
12 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 12
13 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 13
14 Chemical Organization Theory
15 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] Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 15
16 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)] Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 16
17 Practical View 4 4 Chemical 1 Organization 1 Theory Reaction network Organization Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 17
18 All Organizations Organization 4 4 Chemical 1 Organization 1 Theory Reaction network Organizations Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 18
19 Lattice of Organizations Hasse diagram of the organizations 4 {1,2,3,4} Chemical Organization Theory {1} {2, 3} { } Reaction network Organizations Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 19
20 Generate Organization Hasse diagram of the organizations 4 {1,2,3,4} Chemical Organization Theory {1} {2, 3} { } Reaction network G O ({3, 4}) =? Organizations Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 20
21 Generate Organization Hasse diagram of the organizations 4 {1,2,3,4} Chemical Organization Theory {1} {2, 3} Reaction network generate organization G Org ({3, 4}) = {1} { } Organizations Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 21
22 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 22 { } Organizations
23 Self-maintenance Organization := closed & self-maintaining set of (molecular) species Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 23
24 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 -> Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 24
25 Example 1 Organization {a, b, d} 2 b a d e 2 c Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 25
26 Example 1 Organization {a, b, d} 2 b a d e 2 c Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 26
27 Example 1 Organization {a, b, d} 2 b 1. Find flux vector outside of org. = 0 a d 0 e c Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 27
28 Example 1 1 Organization {a, b, d} 2 b Find flux vector 10 a 1 d 1 0 e 0 outside of org. = 0 inside of org. > c Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 28
29 Example 1 1 Organization {a, b, d} 2 b Find flux vector 10 a 1 d 1 0 e 0 0 outside of org. = 0 inside of org. > c Check production rates outside of org. = 0 (closure) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 29
30 Example Organization {a, b, d} 2 b 10 0 a d 1 0 e 1. Find flux vector outside of org. = 0 0 inside of org. > c Check production rates outside of org. = 0 (closure) inside of org. 0 (self-maint.) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 30
31 Example 1 All Organizationen 2 b a d e 2 c Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 31
32 Example 1 All Organizationen 2 b a d e 2 c a Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 32
33 Example 1 All Organizationen 2 b a d e 2 c a b d a Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 33
34 Example 1 All Organizationen 2 b a d e 2 c a b d a c d a Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 34
35 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 35
36 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 36
37 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 = { a, b, d } a b d Hasse diagram of organizations a b c d e a c d Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 37 a Dittrich/Speroni d.f., Bull. Math. Biol., 2007
38 Q1 How does the lattice of organizations of an organism looks like? organizational structure = lattice of organizations Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 38
39 Trivially, all organisms have at least one organization S O 2 W S + O 2O + W S O W {S, O, W} {S} Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 39
40 Is there more? S + O 1 2O 1 + W S + O 2 2O 2 + W S O W Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 40
41 Is there more? S + O 1 2O 1 + W S + O 1 + O 2 2O 2 + W S O W Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 41
42 How does the lattice organizations in an organism looks like? number? hight? size distribution? Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 42
43 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 43
44 Population Dynamics HIV Immunesystem Model
45 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 45
46 HIV Dynamics: Mathematical analysis Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 46
47 HIV Immunsystem Populationsmodell T-Zelle infizierte T-Zelle CTL-Pre CTL-Ef Modell nach: C.D. Wodarz, M. A. Nowak, PNAS 96 (1999), Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 47
48 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), Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 48
49 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), Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 49
50 HIV Immunsystem Populationsmodell T-Zelle infizierte T-Zelle CTL-Pre CTL-Ef Modell nach: C.D. Wodarz, M. A. Nowak, PNAS 96 (1999), Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 50
51 HIV Immunsystem Populationsmodell T-Zelle infizierte T-Zelle CTL-Pre CTL-Ef Modell nach: C.D. Wodarz, M. A. Nowak, PNAS 96 (1999), Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 51
52 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), Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 52
53 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) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 53
54 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) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 54
55 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) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 55
56 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) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 56
57 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) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 57
58 Compare models N. Matsumaru, F. Centler, P. Speroni di Fenizio, P. Dittrich (2006); it - Information Technology, 48(3):1-9, Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 58
59 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) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 59
60 Application of Organization Theory to Planetary Photochemistries Mars 31 molecular species, 103 reactions main component: CO 2 (95%) Y. L. Yung and W. B. DeMore (1999) Photochemistry of Planetary Atmospheres,Oxford University Press Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 60
61 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 61
62 Mars at Night 13 molecules Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 62
63 Mars at Daytime Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 63
64 Distribution of Organizations Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 64
65 Randomizing the Network at daytime Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 65
66 How does the lattice of organizations of an organism looks like?? Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 66
67 Metabolic Models network from Palsson et al (?) analysis by C. Kaleta Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 67
68 E. Coli Metabolism Model Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 68
69 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, Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 69
70 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 70
71 Chemical Evolution Overview Organizations in Space Chemical Information Processing and Chemical Programming Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 71
72 Q2 How did the bio-chemical organization of the pre-prebiotic soup evolved? What is the characteristics of the organizational evolution? upward? downward? Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 72
73 A View of Chemical Evolution Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 73
74 Actual Evolution Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 74
75 Actual Evolution Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 75
76 Actual Evolution vs. Organizational Evolution
77 Organizational Evolution Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 77
78 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 78
79 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 79
80 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 80
81 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 81
82 Perspective Change Hasse diagram of the organizations {1,2,3,4} {2, 3} {1} t1 t2 t3 { } [2] [3] Organizations [1] [4] Dynamics Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 82
83 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 Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 83
84 Downward movement Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 84
85 Upward Movements (adding mutations) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 85
86 Q2 How did the bio-chemical organization of the pre-prebiotic soup evolved? What is the characteristics of the organizational evolution? upward? downward? Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 86
87 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) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 87
88 Space Space plays a fundamental role in many natural bio-chemical processes
89 Organizations in Space Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 89
90 Membranes Clusters Waves Spatial Scales Aspects of Space Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 90
91 Space [P. Speroni di Fenizi, P. Dittrich, Chemical Organizations at Different Spatial Scales, LNCS, Springer, 2007] Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 91
92 Chemical Computing Chemical Programming
93 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 D d C c B b A a D } B,c,C, d, A,b, a, M = { 256 possible sets of molecular species
94 Chemical Flip-Flop (with two inputs) Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 94
95 Flip-Flop dynamics Frankfurt, FIAS Peter Dittrich - FSU & JCB Jena 95
96 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) A, DFG (German Research Foundation) Grant Di 852/4-1
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