Origin of catalytic cycles Peter Schuster Institut fr Theoretische - - PowerPoint PPT Presentation

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Origin of catalytic cycles Peter Schuster Institut fr Theoretische Chemie, Universitt Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA Open Questions on the Origin of Life San Sebastian, 20. 23.05.2009 Web-Page for

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Origin of catalytic cycles

Peter Schuster

Institut für Theoretische Chemie, Universität Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA

Open Questions on the Origin of Life San Sebastian, 20.– 23.05.2009

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Web-Page for further information: http://www.tbi.univie.ac.at/~pks

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1977 1988 1971

Chemical kinetics of molecular evolution

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The Bethe - vonWeizsäcker catalytic cycle ist responsible – in part – for the energy production in massive stars.

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The tricarboxylic acid or citric acid cycle is fuelling the metabolic reactions of the cell.

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The citric acid

r Krebs cycle

(enlarged from previous slide).

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A B C D E F G H I J K L 1

Biochemical Pathways

2 3 4 5 6 7 8 9 10

The reaction network of cellular metabolism published by Boehringer-Ingelheim.

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Complementary () replication of RNA as an example

f an autocatalytic cycle.

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Hypercycles with one and two members are common in nature.

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Hypercycle dynamics for n=3

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Hypercycle dynamics for n=4

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Hypercycle dynamics for n=6

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Chemical kinetics of replication and mutation as parallel reactions

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A fitness landscape including neutrality

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Motoo Kimura

Is the Kimura scenario correct for frequent mutations?

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dH = 1

5 . ) ( ) ( lim

2 1

= =

→

p x p x

p

dH = 2

a p x a p x

p p

− = =

→ →

1 ) ( lim ) ( lim

2 1

dH ≥3

random fixation in the sense of Motoo Kimura Pairs of genotypes in neutral replication networks

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Neutral network: Individual sequences n = 10, = 1.1, d = 1.0

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Consensus sequence of a quasispecies of two strongly coupled sequences of Hamming distance dH(Xi,,Xj) = 1.

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Neutral network: Individual sequences n = 10, = 1.1, d = 1.0

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Consensus sequence of a quasispecies of two strongly coupled sequences of Hamming distance dH(Xi,,Xj) = 2.

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N = 7 Neutral networks with increasing : = 0.10, s = 229

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N = 24 Neutral networks with increasing : = 0.15, s = 229

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N = 70 Neutral networks with increasing : = 0.20, s = 229

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Web-Page for further information: http://www.tbi.univie.ac.at/~pks

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