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In silico optimization in the flow reactor: Evolutionary Trajectory

28 neutral point mutations during a long quasi-stationary epoch Transition inducing point mutations Neutral point mutations leave the change the molecular structure molecular structure unchanged Neutral genotype evolution during phenotypic stasis

Evolutionary trajectory Spreading of the population on neutral networks Drift of the population center in sequence space

Spreading and evolution of a population on a neutral network: t = 150

Spreading and evolution of a population on a neutral network : t = 170

Spreading and evolution of a population on a neutral network : t = 200

Spreading and evolution of a population on a neutral network : t = 350

Spreading and evolution of a population on a neutral network : t = 500

Spreading and evolution of a population on a neutral network : t = 650

Spreading and evolution of a population on a neutral network : t = 820

Spreading and evolution of a population on a neutral network : t = 825

Spreading and evolution of a population on a neutral network : t = 830

Spreading and evolution of a population on a neutral network : t = 835

Spreading and evolution of a population on a neutral network : t = 840

Spreading and evolution of a population on a neutral network : t = 845

Spreading and evolution of a population on a neutral network : t = 850

Spreading and evolution of a population on a neutral network : t = 855

1. RNA phenotypes 2. Genotype-phenotype mappings 3. Evolution on neutral networks 4. Genetic and metabolic networks 5. A glimpse of chemical kinetics and dynamics 6. How do model metabolisms evolve?

Genotype GCGGATTTAGCTCAGTTGGGAGAGCGCCAGACTGAAGATCTGGAGGTCCTGTGTTCGATCCACAGAATTCGCACCA A model genome with 12 genes 1 2 3 4 5 6 7 8 9 10 11 12 Regulatory protein or RNA Regulatory gene Enzyme Structural gene RNA secondary structure Metabolite Genetic and metabolic network RNA spatial structure Three different genotype-phenotype mappings

The search for more complex phenotypes inevitably leads from evolvable molecules to genetic regulation and metabolism. The simplest systems of this kind are artificial regulatory systems on plasmids that can be expressed and studied in Escherichia coli cells.

A model genome with 12 genes 1 2 3 4 5 6 7 8 9 10 11 12 Regulatory protein or RNA Regulatory gene Enzyme Structural gene Metabolite Sketch of a genetic and metabolic network

A model genome with 12 genes 1 2 3 4 5 6 7 8 9 10 11 12 Genetic regulatory network Metabolic network Regulatory protein or RNA Regulatory gene Enzyme Structural gene Metabolite Proposal of a new name: Gen etic and met abolic network

A B C D E F G H I J K L Biochemical Pathways 1 2 3 4 5 6 7 8 9 10 The reaction network of cellular metabolism published by Boehringer-Ingelheim.

The citric acid or Krebs cycle (enlarged from previous slide).

1. RNA phenotypes 2. Genotype-phenotype mappings 3. Evolution on neutral networks 4. Genetic and metabolic networks 5. A glimpse of chemical kinetics and dynamics 6. How do model metabolisms evolve?

A + B � X Stoichiometric equations 2 X � Y Sequences Y + X � D Vienna RNA Package SBML – systems biology markup language d d a b Structures and kinetic = = − k a b 1 d t d t parameters Kinetic differential equations d x = − − 2 k a b k x k x y 1 2 3 d t d y = 2 − ODE Integration by means of CVODE k x k x y 2 3 d t d d = k x y 3 d t Solution curves x i (t) Concentration t Time The elements of the simulation tool MiniCellSim SBML : Bioinformatics 19 :524-531, 2003; CVODE : Computers in Physics 10 :138-143, 1996

ATGCCTTATACGGCAGTCAGGTGCACCATT...GGC DNA string genotype TACGGAATATGCCGTCAGTCCACGTGGTAA...CCG genotype-p h e not y p mapping e m RNA RNA genetic regulation network RNA and protein structures Protein enzymes and small metabolic reaction network Metabolism molecules transport system cell membrane Recycling of molecules environment nutrition waste The regulatory logic of MiniCellSym

The model regulatory gene in MiniCellSim

The model structural gene in MiniCellSim

Cross-regulation of two genes

n p = Activation : ( ) j F p + i j n K p j K = Repression : ( ) F p + n i j K p j = , 1 , 2 i j Gene regulatory binding functions

= = = dq [ G ] [ G ] const . g = Q − Q 1 ( ) 1 2 0 k F p d q 1 1 2 1 1 = = [ Q ] , [ Q ] , dt q q 1 1 2 2 = = [ P ] , [ P ] p p dq = − 1 1 2 2 Q Q 2 ( ) k F p d q 2 2 1 2 2 dt n p = Activation : ( ) j F p dp + i j n = − P P K p 1 k q d p j 1 1 2 1 dt K = Repression : ( ) F p + n i j dp K p = − P P 2 j k q d p 2 2 2 2 = , 1 , 2 dt i j − ϑ ϑ = = ϑ Stationary points : ( ( )) 0 , ( ) p F F p p F p 1 1 1 2 2 1 2 2 2 1 Q P Q P k k k k ϑ = ϑ = 1 1 , 2 2 1 2 Q P Q P d d d d 1 1 2 2 Qualitative analysis of cross-regulation of two genes

+ + + + + = Q Q P P ( ε ) ( ε ) ( ε ) ( ε ) 0 d d d d D 1 2 1 2 Eigenvalues of the Jacobian of the = − Γ Q Q P P ( , ) D k k k k p p cross-regulatory two gene system 1 2 1 2 1 2

+ + + + + = Q Q P P ( ε ) ( ε ) ( ε ) ( ε ) 0 d d d d D 1 2 1 2 Eigenvalues of the Jacobian of the = − Γ Q Q P P ( , ) D k k k k p p cross-regulatory two gene system 1 2 1 2 1 2

= − Q Q P P D d d d d trans 1 2 1 2 + + + + + + Q Q Q P Q P Q P Q P P P ( )( )( )( )( )( ) d d d d d d d d d d d d = 1 2 1 1 1 2 2 1 2 2 1 2 D Hopf + + + Q Q P P 2 ( ) d d d d 1 2 1 2

Regulatory dynamics at D < D Hopf , act.-repr., n=3

Regulatory dynamics at D > D Hopf , act.-repr., n=3

Hill coefficient: n Act.-Act. Act.-Rep. Rep.-Rep. 1 S , E S S 2 E , B(E,P) S S , B(P 1 ,P 2 ) 3 E , B(E,P) S , O S , B(P 1 ,P 2 ) 4 E , B(E,P) S , O S , B(P 1 ,P 2 )

An example analyzed and simulated by MiniCellSim The repressilator : M.B. Ellowitz, S. Leibler. A synthetic oscillatory network of transcriptional regulators. Nature 403 :335-338, 2002

Stable stationary state Hopf bifurcation Increasing Limit cycle oscillations inhibitor strength Bifurcation to May-Leonhard system Fading oscillations caused by a stable heteroclinic orbit

P 1 start start P 3 P 2 The repressilator limit cycle

P 1 Bifurcation from limit cycle � 2 <0 to stable heteroclinic orbit at � 2 � 2 =0 � 1 P 2 Stable heteroclinic orbit � 2 >0 � 2 P 2 � 1 Unstable heteroclinic orbit P 3 P 2 The repressilator heteroclinic orbit

1. RNA phenotypes 2. Genotype-phenotype mappings 3. Evolution on neutral networks 4. Genetic and metabolic networks 5. A glimpse of chemical kinetics and dynamics 6. How do model metabolisms evolve?

Evolutionary time: 0000 Number of genes : 12 06 structural + 06 regulatory Number of interactions : 15 04 inhibitory + 10 activating + + 1 self-activating A genabolic network formed from a genotype of n = 200 nucleotides

Evolutionary time scale [generations]: 0000 initial network Evolutionary time : 0000 , initial network 20 TF00 TF01 TF02 TF03 15 SP04 TF05 SP06 SP07 10 SP08 SP09 TF10 SP11 5 Stationary state 0 100 1000 10000 1e+05 Intracellular time Intracellular time scale

Evolution of a genabolic network : Initial genome: random sequence of length n = 200 , AUGC alphabet Gene length: n = 25 Simulation with mutation rate: p = 0.01 Evolutionary time unit >> intracellular time unit

Number of genes : total / structural genes regulatory genes

Evolution of a genabolic network : Initial genome: random sequence of length n = 200 , AUGC alphabet Gene length: n = 25 Simulation with mutation rate: p = 0.01 Evolutionary time unit >> intracellular time unit Recorded events: (i) Loss of a gene through corruption of the start signal “ TA ” (analogue of the “ TATA Box”), (ii) creation of a gene, (iii) change in the edges through mutation-induced changes in the affinities of translation products to the binding sites, and change in the class of genes (tf � sp). (iv)