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Dynamische Strukturbildung und Systemrisiko in biologischen Systeme - - PowerPoint PPT Presentation
Dynamische Strukturbildung und Systemrisiko in biologischen Systeme - - PowerPoint PPT Presentation
Dynamische Strukturbildung und Systemrisiko in biologischen Systeme Peter Schuster Institut fr Theoretische Chemie, Universitt Wien, Austria and The Santa Fe Institute, Santa Fe, New Mexico, USA BBAW Workshop ber systemische Risiken
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Web-Page für weitere Informationen: http://www.tbi.univie.ac.at/~pks
Peter Schuster. 2015. Ebola – Challenge and Revival of Theoretical Epidemiology. Complexity 20(5):7-12 Peter Schuster. 2016. Major Transitions in Evolution and Technology. Complexity 21(4):7-13 Peter Schuster. 2016. Some Mechanistic Requirements for Major Transitions. Phil.Trans.R.Soc.B 371(1701):e20150439 Peter Schuster. 2016. Increase in Complexity and Information through Molecular
- Evolution. Entropy 18(11):e397
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What distiguishes biology from chemistry?
Autocatalysis is rare in chemistry but obligatory in biology. Biological organisms store information in encoded form and have a record of their history. Particle numers are large in chemistry and small in biology. Stochastic phenomena have relatively little importance in chemistry but dominate biology.
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Sources of risk relevant uncertainties in predictions: (i) exponential growth, (ii) complex internal dynamics, (iii) multiple quasistationary states, (iv) reintroduction of extiguished species.
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Autocatalysis, exponential growth, and prediction
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growth l exponentia ) ( ) (
t f
e N t N x f t d N d = ⇒ =
(A) + X = 2 X
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Pierre-François Verhulst, 1804 - 1849
The logistic equation has been conceived in 1838.
( )
t f
e C C t C f t d d
−
− + = ⇒ − = ) ( ) ( ) ( ) ( 1 ξ ξ ξ ξ ξ ξ ξ
( )
t f
e N C N C N t N C N N f dt dN
−
− + = ⇒ − = ) ( ) ( ) ( ) ( 1
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Logistic growth with different carrying capacity: C = , 1000, 800, 600, 400
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Enlargment of the logistic curves: C = , 1000, 800, 600, 400
A.A. King, M.D. de Cellès, F.M.G. Magpantay, P. Rohani. Avoidable errors in the modelling of outbreaks of emerging pathogens, with special reference to
- Ebola. Proc.Roy.Soc.B 282:e20150347
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Complex dynamics and prediction
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R I dt dR I I E dt dI E E I S dt dE S I S dt dS µ γ µ γ ε µ ε β µ β α − = − − = − − = − − =
The SEIR model of theoretical epidemiology
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The SEIR model: ODE integration and stochastic simulation
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Stochastic phenomena at small particle numbers
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Reproduction and catalyzed reproduction of two species
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Stochastic simulation: D.T. Gillespie, Annu.Rev.Phys.Chem. 58:35-55, 2007
Stochastic modeling of chemical and biological systems
Peter Schuster. Stochasticity in Processes. Fundamentals and Applications in Chemistry and Biology. Springer-Verlag, Berlin 2016
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phase I: raise of [A] phase II: random choice of quasistationary state phase III: convergence to the quasistationary state phase IV: fluctuations around the quasistationary state
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Random decision in the stochastic process n = 2
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Competition and cooperation with n = 2
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Choice of parameters: k1 = 0.011 [M-1t-1]; k2 = 0.009 [M-1t-1]; l1 = 0.0050 [M-2t-1]; l2 = 0.0045 [M-2t-1]; a0 = 200; r = 0.5 [Vt-1]; a(0) = 0
Competition and cooperation with n = 2
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expectation values and 1-bands a(0) = 0, x1(0) = x2(0) = 1 a(0) = 0, x1(0) = x2(0) = 10
choice of parameters: a0 = 200, r = 0.5 [Vt -1] k1 = 0.09 [M-1t -1], k2 = 0.11 [M-1t -1], l 1 = 0.0050 [M-2t -1], l2 = 0.0045 [M-2t -1]
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Reintroduction of extinguished species through mutation
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Catalytic hypercycles
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Second order autocatalysis: hypercycles in the flow reactor
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n = 5 n = 4
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A molecular mechanism for mutation
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mutation rate: p = 0.0000
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mutation rate: p = 0.0010
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mutation rate: p = 0.0020
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Danke für die Aufmerksamkeit!
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Web-Page für weitere Informationen: http://www.tbi.univie.ac.at/~pks
Peter Schuster. 2015. Ebola – Challenge and Revival of Theoretical Epidemiology. Complexity 20(5):7-12 Peter Schuster. 2016. Major Transitions in Evolution and Technology. Complexity 21(4):7-13 Peter Schuster. 2016. Some Mechanistic Requirements for Major Transitions. Phil.Trans.R.Soc.B 371(1701):e20150439 Peter Schuster. 2016. Increase in Complexity and Information through Molecular
- Evolution. Entropy 18(11):e397
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