karl sigmund‘s birthdaypks/presentation/wien-karl70-math15.pdf · karl sigmund‘s birthday peter...
TRANSCRIPT
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Karl Sigmund‘s Birthday
Peter Schuster
Institut für Theoretische Chemie, Universität Wien, Austria and
The Santa Fe Institute, Santa Fe, New Mexico, USA
Symposium in Honor of Karl Sigmund
Wien, 29. - 30.10.2015
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Web-Page for further information:
http://www.tbi.univie.ac.at/~pks
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Karl Sigmund
70 Happy birthday
ad multos annos
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Café Stadlmann, Währingerstraße 26, 1090 Wien
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The interior of Café Stadlmann in the 1930th
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Café Stadlmann before it was closed for ever
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Modeling Cooperation
From Molecules to Man
Peter Schuster
Institut für Theoretische Chemie, Universität Wien, Austria and
The Santa Fe Institute, Santa Fe, New Mexico, USA
Symposium in Honor of Karl Sigmund
Wien, 29.10.2015
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Web-Page for further information:
http://www.tbi.univie.ac.at/~pks
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1. Hypercycles – 1975
2. Hypercycles – 40 years later
3. How important is recycling?
4. RNA replication without protein enzymes
5. Thoughts on major transitions
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1. Hypercycles – 1975
2. Hypercycles – 40 years later
3. How important is recycling?
4. RNA replication without protein enzymes
5. Thoughts on major transitions
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p ...... mutation rate per site and replication
DNA replication and mutation
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RNA or DNA replication dynamics is now fully resolved in chemical kinetic terms but highly complicated and
involving thousands of elementary steps.
Albert Einstein (?): „Things should be made as simple as possible but not simpler!“
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first order autocatalysis Xi …… template
second order autocatalysis Xi … template, Xj … catalyst
competition and selection
rich dynamics including oscillations. multiple stationary states, and
deterministic chaos
competition and cooperation
simple, „linear“ dynamics
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The catalytic hypercycle a model for cooperation
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eigenvalues and eigenvectors
qualitative analysis of hypercycle dynamics
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n = 3: eigenvalues 2,3 = ( -1 i 3) / 2
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n = 4: eigenvalues 2-4 = ( i , -1, -i )
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n = 5: eigenvalues 2-5 = ( 5 -1 (55)/2))/4
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hypercycle in the flow reactor
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flow reactor: n = 4
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flow reactor: n = 5
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1. Hypercycles – 1975
2. Hypercycles – 40 years later
3. How important is recycling?
4. RNA replication without protein enzymes
5. Thoughts on major transitions
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deterministic and stochastic chemical reaction A B
thermodynamic equilibrium
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,
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deterministic and stochastic chemical reaction A + X 2 X
thermodynamic equilibrium
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autocatalysis in the flow reactor
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hypercycle in the flow reactor
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Competition between the absorbing and the quasi-stationary state
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flow reactor: n = 4
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flow reactor: n = 4
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flow reactor: n = 5
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1. Hypercycles – 1975
2. Hypercycles – 40 years later
3. How important is recycling?
4. RNA replication without protein enzymes
5. Thoughts on major transitions
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Replicator equations in different environments
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open systems for studying evolution in vitro I
serial transfer flow reactor
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open systems for studying evolution in vitro II
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recycling open systems for studying evolution in vitro
„Los Alamos bug“
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A + X 2 X ; X D
A + X 2 X ; X D ; D A
Shneior Lifson and recycling in origin of life models
Shneior Lifson, 1914 - 2001
recycling
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identical solution curves in growing and stationary systems
dynamics in growing system
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1. Hypercycles – 1975
2. Hypercycles – 40 years later
3. How important is recycling?
4. RNA replication without protein enzymes
5. Thoughts on major transitions
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Science 2009, 323:1229 - 1232
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An example of two ribozymes growing exponentially by cross-catalysis.
T.A. Lincoln, G.F. Joyce. 2009. Self-sustained replication of an RNA enzyme. Science 323:1229-1232
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An example of two ribozymes growing exponentially by cross-catalysis.
T.A. Lincoln, G.F. Joyce. 2009. Self-sustained replication of an RNA enzyme. Science 323:1229-1232
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Nature 2012, 491:72 - 77
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1. Hypercycles – 1975
2. Hypercycles – 40 years later
3. How important is recycling?
4. RNA replication without protein enzymes
5. Thoughts on major transitions
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Scarcity drives optimization in Darwin‘s sense
Abundance is required for innovation and major transitions
Complexity 1996, 2(1):22 - 30
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Manolis Kellis, Bruce W. Birren, and Eric S. Lander. Proof and evolutionary analysis of ancient genome duplication in the yeast Saccharomyces cerevisiae. Nature 428: 617-624, 2004
A model for the genome duplication in yeast 100 million years ago
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Thank you for your attention!
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Web-Page for further information:
http://www.tbi.univie.ac.at/~pks
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