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Karl Sigmunds Birthday Peter Schuster Institut fr Theoretische - - PowerPoint PPT Presentation

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Karl Sigmunds Birthday Peter Schuster Institut fr Theoretische Chemie, Universitt Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA Symposium in Honor of Karl Sigmund Wien, 29. - 30.10.2015 Web-Page for further

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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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Ka Karl l Sig igmun und

70

Happ ppy bi birt rthd hday ad d mul ulto tos anno nnos

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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 (55)/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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  • pen systems for studying evolution in vitro I

serial transfer flow reactor

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  • pen 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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